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The Time Value of Money - Toán Kinh Tế | Trường Đại học Tôn Đức Thắng

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Mai Nguyệt

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The Time Value of Money - Toán Kinh Tế | Trường Đại học Tôn Đức Thắng

26 13 lượt tải Tải xuống

Test ID: 7658669

The Time Value of Money

Question #1 of 87 Question ID: 7 41280

Question #2 of 87 Question ID: 75 412 3

Question ID: 768 412

Question #4 of 87 Question ID: 759 412

Y rr vou bo ow $15,000 b c r. b p d pto uy a a The loan is to e ai off in monthly ayments o er 2% 5 years at 1 annual interest. What is

the amount of ea ayment ch p ?

$4 .56

$ 45 6.

$334.

Explanation

I = 1 1 12 / 2 = ; N = 5 × 12 = 60; PV = 15,000; CPT → PMT 67 = 333. .

W rr dr w ,000ei Z g d w R b k. chan has funds on eposit ith Iron ange an The funds are u ently earning % . w6 interest If he ith a s $15

to hase an automo ile the inte est ate an est thou ht of as n): purc b , 6% r r c be b g a(

discount r .ate

o opp rtunity ost c .

finan in ostc g c .

Explanation

Sin ei ill fo oin inte est on the ith fun s thece W w be reg g r w drawn d , 6% c b b c d c -interest an e est harac zteri e as an opportunity ost

the etu he oul ea ost onin his auto hase until the futu r rn c d rn by p p g purc re.

lo alc b k an offers an account that pays 8%, compounded quarterly, r d $ 0,000 r fo any eposits of 1 o more that are left in the

a a e 5 account for p rio ofd yea Thers. effe tic ve annual ate r of inte estr on this ccount is:

8.24%.

4. %.65

9.01%.

Explanation

(1 + − ) 1 = ( − = 1.02) 1 8.24%.

m 4

Question #5 of 87 Question ID: 81 412 0

Question #6 of 87 Question ID: 412802

Question #7 of 87 Question ID: 81 412 4

s the num of hat is the effe on the A ber , w ct E R? EAR:

in easin atecreases at a decr g r .

in eases at an in easin atecr cr g r .

does not incr .ease

Explanation

The is an limit to the Are upper E R c g . c c g as the frequency of ompoundin increases In the limit, with ontinuous ompoundin the

EAR = e - . H , E1 ence the AR dincreases at a ecr .easing rate

n 7 in estov r s $4,000 in an account that ays p .5%, compounded w w b w rannually. Ho much ill this investment e orth afte

12 yea sr ?

$5,850.

$9,3 .58

$ 29,5 7.

Explanation

N = 12; /Y = ; PI 7.5 V = -4,000; PMT = 0; CPT → FV = $ .9,527

Consi yea annuity that omises to ay out yea i en this is an ina y annuity an that an in estoder a 10- r pr p $1 e0,000 p r r; g v ord r d v r

can earn 10% r , von he money the future alue of this annuity, d 0 at the en of 1 years, would be:

$159,374.

$175,312.

$110.000.

Explanation

N = 10; /Y = I 10; PMT = -10,000; PV = 0; CPT → FV = $159,3 4.7

If ual osits of ma into an in estment ount ea nin 10 eq annual dep $1,000 a er de v acc r g 9% g , w wstartin today ho much ill you have

in yea s 20 r ?

$3 ,204.9

$42, .165

$35,967.

APR

Question #8 of 87 Question ID: 79 412 0

Question #9 of 87 Question ID: 77 412 3

Question #10 of 87 Question ID: 785 412

Explanation

Swit to B mo MTch GN de. P = -1,000; N = 10, /Y = I 9, PV = 0; = CPT → FV 16,560.2 w9. Remember the ans er will one yea be r

afte the last ayment in annuity ue V lemsr p d F prob . Now PV = 16,560.29; N = 0; /Y = 1 I 9; PMT = 0; = 3CPT → FV 9,204.23.

Swit toch back END mo de.

n u 1 in estov r p rchases a 0-year, $1,000 par value on that ays b d p annual ou ons c p of If $100. the ma et aterk r of inte estr is

12%, what is the ma et aluerk v of the on b d?

$1,124.

$950.

Explanation

Note that b j d ond problems are ust mixe annuity problems. You an sol on lems i tly ith you finan ial al ulato c ve b d prob d rec w r c c c r

usin all fi of the main TVM eys at on on ty es of lems the on s ig ve k ce. For b d- p prob b d' pr ce (PV) ill ne ati hile the w be g ve, w

c voupon payment (PMT) and par value (FV) w bill e positi e. N = 10; /Y = I 12; FV = 1,000; PMT = 100; CPT → PV = - .886.99

Giv v r.en: $1,000 in estment, c d 2% d v r ompounde monthly at 1 fin the future alue afte one yea

$ 21,1 1.35.

$ 21,1 6.83.

$1,120.00.

Explanation

Di i the inte est ate y the num of om oun io s an multi ly the num of yea s the num of om ounv de r r b ber c p d per d d p ber r by ber c p d

p d 2erio s. I = 12 / 2 = 1 1; N = (1)(1 ) = 12; PV = 1,000.

n e in estov r d posits in $10,000 a 5 ban ount ayink acc p g % inte est om ounr c p ded annually. Rounded to the nea est olla inr d r, 5

yea s the in esto ill ha e:r v r w v

$12,500.

$10,210.

Explanation

PV = 10,000; /Y = ; I 5; N = 5 CPT → FV = 12, 3.76

Question #11 of 87 Question ID: 9 41280

Question #12 of 87 Question ID: 769 412

Question #13 of 87 Question ID: 786 412

o 1 1r: 0,000( .05) = 12, 3.76

Given the following cash flow stream:

End of Year Annual Cash Flow

1 $4,000

2 $2,000

3 -0-

4 -$1,000

Using r , v c w a 10% discount ate the present alue of this ash flo stream i :s

$4, .6 60

$3,4 .15

$3, .6 63

Explana onti

PV(1): N = 1; /Y = I 10; FV = -4,000; PMT = 0; CPT → PV = 3,636

PV(2): N = 2; I/Y = 10; FV = -2,000; PMT = 0; CPT → PV = 31,65

PV(3): 0

PV(4): N = 4; I/Y = 10; FV = = 0; 1,000; PMT CPT → PV = - 368

Total PV = 3,6 63 + 1,653 + 0 − 68 63 = 4,60

I t t t tf a $45,000 car loan is financed a 12% over 4 years, what is he mon hl eny car paym ?

$1,185.

$985.

$1,565.

Explana onti

N = 4 × 1 82 = 4 ; I/Y = ; P12/12 = 1 V = -45,000; FV = 0; CPT → PMT 185 = 1, .02

Find v g c w . d . the future alue of the followin uneven ash flo stream Assume en of the year payments The d riscount ate is 12%.

Year 1 -2,000

Year 2 -3,000

Question #14 of 87 Questi ID:on 4 21278

Question #15 of 87 Questi ID:on 412811

Y ,000ear 3 6

Y ,000ear 4 25

Year 5 30,000

$33,004. .15

$58,164. .58

$65,144.33.

Explana onti

N = 4; I/Y = 12; PMT = 0; PV = -2,000; CPT → FV = -3,147.04

N = 3; I/Y = 12; PMT = 0; PV = -3,000; CPT → FV = -4,214.78

N = 2; I/Y = 12; PMT = 0; PV = 6,000; CPT → FV = 7,526.40

N = 1; /Y = I 12; PMT = 0; PV = 25,000; CPT → FV = 28,000.00

N = 0; I/Y = 12; PMT = 0; PV = 30,000; CPT → FV = 30,000.00

S w 4. .um the cash flo s: $58,16 58

l na al ula on solu onter tive c c ti ti : -2,000 × ,000 × 1.12 − 3,000 × 1.12 + 6 1.12 + 25 1,000 × 1. 2 + 30,000 = $58,16 584. .

I t t t t t t t t tf $10,000 is inves ed in a mu ual fund ha re urns 12% per yea afr, er 30 years he i tmnves en will be wor h:

$300,000.

$10,120.

$2 .99,599

Explana onti

FV = 1 1 10,000( . 2) = 299,599

Using TI BAII Plus: N = 30; I/Y = 12; PV = -10,000; CPT → FV = 2 .99,599

n e o e e o n a annu llity i w pay ight annual of $100, with the first payment t b re ec iv d one year fr m no hew. I tf i terest r te

i i i itys 12% per yea har, w t s the esen pr t value of th s annu ?

$1,229.97.

$556.38.

$4 .96.76

Explana onti

N = 8; /Y = I 12%; PMT = -$100; FV = 0; CPT → PV = $4 .96.76

4 3 2

Question #16 of 87 Questi ID:on 4 41279

Question #17 of 87 Questi ID:on 412756

Question #18 of 87 Questi ID:on 412 28 8

ssu oun of ea of annual en s has he eseming a disc t ra et 10%, which str m paym t t highest pr nt value?

$20 -$5 $20 $110

-$ 00100 -$100 -$100 $5

$110 $20 $ 0 $1 5

Explana onti

This is an n i tu on uiti q es hetion. T two c w ash flo stream as th t contain the $110 paym ne t have the same total a flo c sh w but the correct

answer is the one where the $110 occ ru s earlier. c w The ash flo stream a th t has the $ 00 5 that occ ru s four years hence is overwhe elm d by

the large negative flows that precede it.

The s real ri k-free rate can ou be th ght of as:

approximately the nominal ris tek-free ate r plus the expec d inflation rate.

e e e e exactly the nom nali risk-free rate r duc d by the xp cted ri tinfla on ate.

Explana onti

The a o a appr ximate rela onti ship between a nom nali r tes, real r tes an nfla on and d exp ce te i ti rates c be written s:

Nominal risk-free rate = risk-free rate expected inflation real + rate.

The er fo anre w ce rewrit ie th s equati ion n terms of the real risk-free rate as:

Real risk-free rate risk-free rate - expected inflation rate = Nominal

The e xact rela onti is: (1 + real)(1 + e expect d i tinfla on) = ( + 1 nom nali )

n n o o n o n n i vest r wh requires an ann alu retur of 12% has the ch i i ice of rece v g one of the followi g:

A y. 10 annual pa ments of $1,225.00 bto egin at t he end of on e year.

B y 97 96 y. 10 annual pa ments of $1,0 . begi i i inn ng mmed atel .

Which option has the highest present value (PV) y an ma ld approxi te how much greater i its than th he ot er option?

Option B's PV is $114 greater than o tion Ap 's.

Option B's s PV i $27 greater than option A's.

Option A's s PV i $42 greater than option B's.

Question #19 of 87 Qu ID: 778estion 412

Question #20 of 87 Qu ID:estion 412803

Question # 1 of 872 Qu ID: 79estion 412 3

Explana onti

Option A: N = 10, PMT = -$ = 1,225, I 12%, FV = 0, Compute PV = $6, .921 52.

Option B: N = 9 1 1, PMT = -$ ,097.96, I = 2%, FV = 0, Compute PV → $5,850. ,051 + 1 97.96 = 6 u,948.17 or put calc la ntor i

Begin mode N = 10, PMT = $1,097.96, I = 12%, FV = 0, Compute PV → $6, .948 17. b =Difference etween the 2 options

$ 2 46,9 1.52 − $6,9 8.17 = -$2 .6.65

Option B's PV is approximately $27 higher than option A's PV.

lo alc b k an offers a certificate of d (eposit CD) t tha earns 5.0% compounded quarterly for three and one half years. If a

d pe o osit r places $ ,000 d5 on eposit, what w bill e the value of the acco nu t at maturity?

$ 3 05,9 1. 6.

$ 45,9 9.77.

$5,875.00.

Explana onti

Th ye value of the accou unt at mat rit will be: $5,000 × (1 + 0.05 / 4) = $ ;5.949.77

o ar with financial al la c cu tor: N = 3 years × 4 q = uarters/year + 2 = 14 periods; I 5% / 4 quar rte s/year = 1.25; PV = $5,000;

PMT = 0; = $ .CPT → FV 5, .949 77

Justin Banks j wust on the lottery and g d b c r p .is tryin to ecide etween the ann alu ash flow payment option o the lum sum option

He c % b k d c w $ g r an earn 8 at the an an the ann alu ash flo option is 100,000/year, begi inn n today fo 15 years. What is the

ann al flo on anu cash w opti worth to B ks today?

$ 4855,9 7.87.

$924,423.70.

$1,080,000.00.

Explana onti

First p r u ut yo r calculato in the BGN.

N = 15; /Y = ; PI 8 MT = 100,000; CPT → PV = 924,423. 0.7

l na l no al la l l l na ann of anter tive y, do t set your c cu tor to BGN, simp y mu tip y the ordi ry uity (end the period payments) swer by 1

+ /Y. YI o n ou h get t e annuity due an an onswer d you d 't ru the r k is of forgettin og t reset your cal lacu t r ba ock t the end of the

period setting.

OR N = 14; /Y = ; PI 8 MT = 100,000; CPT → PV = 824,423. 24,423. 0.70 + 100,000 = 9 7

(3.5 × 4)

Question #22 of 87 Qu ID:estion 485754

Qu ID: 81estion 412 2

Th ye follo am ofwing stre cash flo llws wi occur d at t he en of the next five ears.

Yr 1 -2,000

Yr 2 -3,000

Yr 3 6,000

Yr 4 25,000

Yr 5 30,000

t t t t t t t t a disco nu ra e of 12%, he presen value of his s ca h flow s ream is closest o:

$33,004.

$58,165.

$3 .6,965

Explana onti

N = 1; /Y = I 12; PMT = 0; FV = -2,000; CPT → PV = - .1,785.71

N = 2; I/Y = 12; PMT = 0; FV = -3,000; CPT → PV = -2,3 .91.58

N = 3; I/Y = 12; PMT = 0; FV = 6,000; CPT → PV = 4,270. .68

N = 4; I/Y = 12; PMT = 0; F = 2V 5,000; CPT → PV = 15 887 95, . .

N = 5; /Y = I 12; PMT = 0; FV = 30,000; CPT → PV = 17,022. .81

S w .um the cash flo s: $33,004.15

Note: If you ant w to use you al ulato sr c c r' NPV fun tionc to solve this problem, you need to enter zero as the initial cash flow

(CF ). F , If you enter -2,000 as C all your cash flow w .s w b p d d w g g ill e one erio too soon an you ill et one of the wron ans ers

P ccaul K r $ 0,000 b k ohle inherits 5 and deposits it immediately in a an a ount that p % rays 6 interest. No other deposits o

w dr w w cc c g?ith a als are made. In t o years, what w bill e the a ount balan e assuming cmonthly ompoundin

$53,100.

$50,500.

$56,400.

Explanation

To om oun monthly emem to i i the inte est ate an the num of io s ill yea s c p d , r ber d v de r r by 12 (6%/12 = 0.50%) d ber per d w be 2 r

times months io s) The alue afte io is 56 57 99 12 (2 × 12 = 24 per d . v r 24 per ds $50,000 × 1.005 = $ ,3 . .

The lem an also sol usin the time alue of money fun tions MT prob c be ved g v c : N = 24; I/Y = 0.5; P = 0; PV = 50,000; CPT F =V

$56,3 .57.99

n e e annuity ill ay w p ei htg annual ayments p of ith $100, w the fi st aymentr p to b receiv d th eer years from no Ifw. the inte estr

0 0

Question #24 of 87 Question ID 787 : 412

Question # 5 of 872 Question ID 799 : 412

Question # 6 of 872 Question ID 79 : 412 2

rate is 12% p prer year, what is the present v ? alue of this annuity The esent value of:

a lum sum p dis ountec d for 2 years, where the lump sum is the esent pr value of

an ord r r 2%.ina y annuity of 8 pe iods at 1

a lum sum is ounte fo yea sp d c d r 3 r , where the lum sump is the present alue v of an

ordina yr annuity of 8 e p riods at 12%.

an ina y annuity of io s at ord r 8 per d 12%.

Explanation

The V P of an ordinary annuity (cal ulationc END mode) g v p p p ,ives the alue of the ayments one eriod before the first ayment

w chi h is a time = 2 v = 0 value here. gTo et a time alue, v b d d r p ( .this alue must e iscounte fo two eriods years)

What is the ma imum an x investor should be willing pto ay fo r an annuity that ay out 1 will p $ 0,000 at the beginning of each of the ne xt 10

years, given the investor wants to ea rn 1 5 om oun e 2. %, c p d d annually?

$62,2 .85

$52,2 .85

$55,364.

Explanation

Using END mo the V de, P of this annuity due is $10,000 plus the esent pr value of a 9-year ordinary annuity: N=9; I/Y= 2. ;1 5

P =- PMT 10,000; FV=0; C T PV 85 85=$52,2 ; $52,2 + $10,000 = $62,2 .85

Or set you al ulato tor c c r B moGN de then N=10; I/Y=12.5; PMT V=-10,000; F =0; PCPT V= $62,2 .85

W 0-hat is the present value of a 1 year, $100 d rannual annuity ue if interest ates are 0%?

N .o solution

$1,000.

$900.

Explanation

W d.hen I/Y = 0 jyou ust sum up the numbers since there is no interest earne

If yea is in este at the en of ea of the ne yea in eti ement ount yiel in ho mu ill an $2,000 a r v d d ch xt 45 rs a r r acc d g 8.5%, w ch w

in esto ha at eti ement yea s om to ayv r ve r r 45 r fr d ?

Question # 7 of 872 Question ID 755 : 412

Question # 8 of 872 Question ID 75 : 412 4

Question # 9 of 872 Question ID 77 : 412 0

$ 3100,1 5.

$ 09 1,0 0.6

$ 090,1 6.

Explanation

N = 45; PMT = -2,000; PV = 0; I/Y = %; 8.5 CPT → FV = $901,0 0. .6 79

Ve esea has een on tin in esto olls fo Thi tate Ban They ha foun the most in esto s not illin toga r rch b c duc g v r p r rd S k. ve d v r a er w g

tie thei money in yea yea CD unless they ei at least mo than they oul on an ina y up r a 1 - r (2- r) rec ve 1.0% (1.5%) re w d ord r

sa in s ount If the sa in s ount ate isv g acc . v g acc r 3%, and b r w r , d bthe ank wants to aise funds ith 2-yea CDs the yiel must e at

least:

4. %, r pr r r r5 and this e esents a equi ed ate of return.

4.0%, d r r r .an this epresents a equired rate of eturn

4. pr5%, d ran this e esents a d r .iscount ate

Explanation

Sin ta in the ie of the minimum amount ui to in in esto s to len fun s to the an this is estce we a e r k g v w req red duce v r d d b k, b

d b pescri ed as a required rate of return. d Base u on the numerical information, r bthe ate must e 4.5% (= 3.0 + 1.5).

S welmer Jones has j d r v Hust inherite some money and wants to set some of it aside fo a acation in a aii one year .from today

H rd cis b p % d . ank will ay him 5 interest on any funds he eposits In o er d w to etermine ho mu h of the money must be set aside

an hel fo the i he shoul use thed d r tr p, d 5% as a:

discount r .ate

r r requi ed rate of retu n.

o opp rtunity ost c .

Explanation

H ce needs to figure out how mu h the trip will c r, d % d r c cost in one yea an use the 5 as a iscount ate to onvert the future ost to a

pr x wesent v . , calue Thus in this onte t the r b vate is est ie ed d r .as a iscount ate

J rgamie Mo an needs to $2,000 . c % b , w in 18 months If she an earn 6 at the ank, quarterly ho much

must she osit to ay dep d ?

$ 21,8 9.08.

Question #30 of 87 Question ID 816 : 412

Question # 1 of 873 Question ID 9 : 41282

Question #32 of 87 Question ID : 485755

$1,832. .61

$1,840.45.

Explanation

E c pra h q r r cuarte of a yea is om ised of 3 months thus N = 18 MT / 3 = 6; I/Y = 6 / 4 = 1.5; P = 0; FV = 2,000; CPT → PV =

$ 21,8 9.08.

R c cc venee F r $2,000 ishe invests ea h year, g r w, rstartin one yea from no in a etirement a ount. If the in estments earn 8% ro

1 o e0% annually v r 30 yea thers, amount ishe ill F r w accumulate is closest to:

8% 10%

$24 0,0005,000 $36

$225,000 $330,000

$22 0,0005,000 $36

Explanation

N = 30; I/Y = 8; PMT = -2,000; PV = 0; = 22CPT FV 6,566.42

N = 30; I/Y = 10; PMT = -2,000; PV = 0; = 32CPT FV 8 988, .05

It ill ost yea fo fou yea s hen an yea ol hil is ea y fo olle mu shoul in este to ay if w c $20,000 a r r r r w 8- r d c d r d r c ge. How ch d be v d d

the hil c d will ma the fi st of fou annual ith als yea om to ay The te ate of etu is ke r r w draw 10- rs fr d ? expec d r r rn 8%.

$66,243.

$30, 3.68

$33, .1 83

Explanation

First, d fin the present v c c d r . (R r Palue of the ollege osts as of the en of yea 9 emembe that the V of an ordinary annuity is as of

time = 0. If the first p r 0, v d d r . N = 4; /Y = ;ayment is in yea 1 then the present alue of the annuity is indexe to the en of yea 9) I 8

PMT = 20,000; CPT → PV = $66,242. c54. Se ond, d vfin the present alue of this single sum: N = 9 8; I/Y = ; FV = 66,242.54;

PMT = 0; CPT → PV = 33, .137.76

n in esto ma esv r k 48 monthly ayments p of ea $500 ch beginnin to ayg d into an account that ill w have a value of $29,000 at the

en of fou yea s The state annual inte est ate isd r r . d r r closest to:

Question #33 of 87 Question ID 18 : 434 4

Question #34 of 87 Question ID 76 : 412 0

Question # 5 of 873 Question ID : 412822

9 5. 0%.

9.00%.

10.00%.

Explanation

Be ause this is an annuity ue ayments at the sta of ea io the al ulato must fi st set to B moc d (p rt ch per d) c c r r be GN de.

N = 48; PMT = 500; FV = -29,000; PV = 0; CPT I/Y = 0.7532

This enta is monthly ate ause the time io s ente as months It must on te to state perc ge a r bec per d we er red 48 . be c ver d a d

annual enta ate A perc ge r ( PR .04%.) b r c p r y multiplying by the numbe of ompounding periods e year: 0.7532 × 12 = 9

stated rinterest ate of 9% compounded r rsemiannually esults in an effective annual ate closest to:

9.3%.

9 1. %.

9.2%.

Explanation

Semiannual r . ate = 0.09 / 2 = 0.045

E vffecti e annual rate = (1 + 0.04 − 5) 1 = 0.09203, r o 9.203%.

lo alc b k an advertises that it w pill ay interest at the rate of 4.5%, compounded , r r monthly on egula savings accounts. What is

the effe ti ate of inte est that the an is ayin on these ounts c ve r r b k p g acc ?

4. %.59

4.50%.

4. %.65

Explanation

(1 + 0.045 / 12) − 1 = − 1.0459 1 = 0.04 .59

S rk rrarah Pa er b g ,000 c r w $ ,000 bis uyin a new $25 ar. He trade-in is orth 5 so she needs to o ow $20,000. The loan w b p dill e ai

in monthly installments an the annual inte est ate on the loan is 48 d r r 7.5%. p d d If the first ayment is ue at the en of the first

month hat is ah monthly ayment, w Sar 's car p ?

$4 0. .8 57

Question # 6 of 873 Question ID 8 : 41280

Question # 7 of 873 Question ID : 412823

Question # 8 of 873 Question ID 6 : 41280

$4 3. .8 58

$4 .16.67

Explanation

N = 48; /Y = / ; PI 7.5 12 = 0.625 V = 20,000; FV = 0; CPT → PMT = 483. .58

n e e in estmentv offe sr $100 p r yea for r ver. If ete P r Walla s ui ate of etu on this in estment is ho mu isce' req red r r rn v 10%, w ch

this in estment th to him v wor ?

$1,000.

$10,000.

$500.

Explanation

For p , Pa erpetuity V = P = MT ÷ I 1 100 ÷ 0.10 = ,000.

H v cc drow d much shoul an in estor rhave in a etirement a ount on his 65 b w wirthday if he ishes to ith aw $40,000 on that

b dirth ay and g , g reach of the followin 14 birthdays assumin his etirement account is exp ce ted to earn 14.5%?

$2 4,422.7

$2 2, .7 977

$234,422.

Explanation

This is an annuity d r GN ue so set your calculato to the B mode. N = ; 15 I/Y = 1 54. ; PMT = -40,000; FV = 0; CPT → PV =

274,422.50. Switch b ck a to EN .D mode

W 2- c %?hat is the present value of a 1 year d p $ ,000 p r dannuity ue that ays 5 e year, given a is ount rate of .7 5

$3 .6,577

$4 .1,577

$3 .8,676

Explanation

Using your calculator: N = 11; I/Y = 7.5; PMT = - = 0; 5,000; FV CPT → PV = 3 + 6,577 5,000 = $4 . r 1,577 O set your calc rulato

to B mo an GN de d N = 12; I/Y = 7.5; PMT = -5,000; FV = 0; CPT → PV = $4 .1,577

Question ID : 412804

Question #43 of 87 Question ID 1 : 41280

Question #44 of 87 Question ID 5 : 41282

Con nin an ina y annuity an an annuity ue ith the same ayments an ositi inte est ate hi of the follo incer g ord r d d w p d p ve r r , w ch w g

statements is ate most accur ?

The elationshire is no r p.

The esent alue of the ina annuity is less than an annuity ue pr v ord ry d .

The esent alue of the ina y annuity is eate than an annuity ue pr v ord r gr r d .

Explanation

W rdith a positive interest r , vate the present alue of an o inary annuity is less than the present v d . alue of an annuity ue The first

cash flow d b g p , c w din an annuity ue is at the eginnin of the eriod, while in an ordinary annuity the first ash flo occurs at the en

of the io The efo ea ash flo of the ina y annuity is is ounte one io mo per d. r re, ch c w ord r d c d per d re.

If ut into an ount at the en of ea $2,500 we er p acc d ch of the ne yea s ea nin 15 inte est ho mu oul in xt 10 r r g % annual r , w ch w d be

the ount at the en of ten yea s acc d r ?

$2 ,4 .7 61

$4 .1,965

$50, .759

Explanation

N = 10; ; PI = 15 MT = 2,500; CPT → FV = $50, .759

Elise Co s he fun mana an i nhill s ie as ently ante mission to ta month sa ati al rr , dge d ger d av d dow k r, w rec gr d per ke a 4 bb c .

Du in the sa ati al s he ule to sta in 11 months) Co ill s i at imately eso ts lo ate in the Aust ianr g bb c , ( c d d rt , rrs w k approx 12 r r c d r ,

Italian an iss Al Co s estimates that she ill, d Sw ps. rr w need $6,000 at the b g eginnin of each month for .expenses that month

(S c vhe has already finan ed r he initial tra el and c H r p r wequipment osts.) e financial lanne estimates that she ill earn an annual

rate of .8 5% d %. Huring r p d d r r d g r he savings erio an an annual ate of eturn urin he sabbatical of .9 5 ow d dmuch oes she nee

to ut in he sa in s ount at the en of ea month fo the ne 11 months to ensu the ash flo she nee s he p r v g acc d ch r xt re c w d over r

sa ati albb c ? Ea e och month Co s shoul sa, rr d v appr ximately:

$2,0 0.7

$2,0 0.8

$2,0 .65

Explanation

This is ste lem i st nee to al ulate the esent alue of the amount she nee he sa ati al This a o tw - p prob . F r , we d c c pr v ds over r bb c . (

amount ill in the fo of an annuity ue sin she ui es the ayment at the innin of the month Then ill use w be rm d ce req r p beg g .) , we w

futu alue fo mulas to ete mine ho mu she nee s to sa ea monthre v r d r w ch d ve ch .

Question # 5 of 874 Question ID 797 : 412

Question # 6 of 874 Question ID 77 : 412 2

Question # 7 of 874 Question ID 757 : 412

Step 1: Calculate present value of amount required during the sabbatical

U c EGsing a finan ial c Salculator: et to B IN , Mode then N = 4; I/Y = 9.5 / 12 = 0.79 671 ; PMT = 6,000; FV = 0; CPT → PV =

-23, .7 91

Step 2: Calculate amount to save each month

U c c ksing a finan ial cal ulator: Ma e sure it is set to END mo thende, N = 11; I/Y = 8.5 / 12.0 = 0.70833; PV = 0; F = 23, ;V 719

CPT → PMT= -2,081, o a or ppr ximately $2,080.

Com ute the esent alue of etuit ith ments innin fou ea s om no ssume the iatep pr v a perp y w $100 pay beg g r y r fr w. A appropr

annual inte est ate is r r 10%.

$1000.

$751.

$683.

Explanation

Com ute the esent alue of the etuit at all the esent alue of etuit annuit is alue one iop pr v perp y (t = 3). Rec , pr v a perp y or y v d per d

before the first payment. So, the present value at t = 3 is 100 / 0. 0 = ,000. N1 1 ow d p it is necessary to iscount this lum sum to t

= 0. Therefore, pr vesent alue at t = 0 is 1,000 / (1.10) = 751.

W x vhat is the ma imum price an in estor wshould be illin to to fo ea annuit that illg pay ( day) r a 10 y r y w g $enerate 500 p re

q duarter (such payments to be ma e at the end of each q wuarter), given he ants to earn 12%, compounded quar rte ly?

$11,557.

$6,440.

$11,300.

Explanation

U c csing a finan ial cal ulator: N = 10 × 4 = 40; I/Y = 12 / 4 = 3; PMT = -500; FV = 0; CPT → PV = .11,557

T-bill yiel s and c be thou htg of as:

real ee ates ontain an inflation risk-fr r because they c premium.

nominal is ee ates ause the not ontain an inflation emium r k-fr r bec y do c pr .

nominal is ee ates ause the ontain an inflation emium r k-fr r bec y c pr .

Explanation

Question # 8 of 874 Q ID 78uestion : 412 0

Question # 9 of 874 Q IDuestion : 412813

Question #50 of 87 Q IDuestion : 412800

T-b v cills are go ernment issued se urities and c d b d r k . are therefore onsidere to e efault is free Mo er precisel they, y a er nominal

r risk-f ee r r r r r rates athe than eal isk-free ates since they c r d .ontain a premium fo exp ce te inflation

c p d . r dertain inv cestment produ t promises to ay $25,458 at the en of 9 years If an investo feels this investment shoul

pr co ud e a rate of r d w g p r ?eturn of 14%, compounde annually, what's the most he should be illin to ay fo it

$7,8 92 .

$9,42 .6

$7,6 81 .

Explanation

N = 9; /Y = I 14; FV = -2 = 0; 5,458; PMT CPT → PV = $7, .828 54.

o 1r: 25,458/ .14 = 7 5,828. 4

If an in esto utsv r p $5,724 per yea sta tin atr, r g the en ofd the fi str yea inr, an account ea ninr g 8% d p an ends u accumulating

$500,000, w d d ho many years i it take the investor?

27 years.

87 y ears.

26 years.

Explanation

I/Y = 8; PMT = -5,724; FV = 500,000; CPT → N = 2 .7

Remember, p p d Fyou must ut the mt in as a negative (cash out) an the V in as ositi ash in to om ute eithe a p ve (c ) c p r N or I/Y.

n in esto illv r w r $ ,000 r r . p b r d . eceive an annuity of 5 a yea fo seven years The first ayment is to e ec vei e 5 year rs f om today If

the annual inte est ate is 11 r r .5%, what is the esent alue of the annuit pr v y?

$13,453.

$23, .185

$15,000.

Explanation

With PMT = 5 7 5,000; N = ; I/Y = 11. ; v (alue at t = 4) = 23,185.175. Therefore, PV (at t = 0 = 23,) 185.175 / (1.115) =

$15,000. .68

Question #51 of 87 Q ID 765uestion : 412

Question #52 of 87 Q ID 776uestion : 412

Question #53 of 87 Q IDuestion : 485753

Question #54 of 87 Q ID 5uestion : 41280

W vhat's the effecti e r r g rate of eturn on an investment that enerates a eturn of 12%, c ?ompounded quarterly

12.00%.

14.34%.

12. %.55

Explanation

(1 + 0. − 12 / 4) 1 = − 1.1255 1 = 0.1255.

In 10 yea hatrs, w is the alue v of in este to $100 v d day at an inte est ater r of 8% per d ?year, compounde monthly

$222.

$2 .16

$180.

Explanation

N = 10 × 2 = 1 120; /Y = I 8/12 = 0.666667; PV = -100; PMT = 0; = 22 .CPT → FV 1.96

If an in estmentv has an APR % d c , rof 18 an is ompounded quarterly its effective annual ate (EAR) is closest to :

18.00%.

19 5.2 %.

18.81%.

Explanation

B y Aecause this in estment is om oun ua te l v c p ded q r r , we nee to i i thed d v de PR by four compounding periods: 18 / 4 = 4.5%.

EAR = (1.04 .2 %.5)4 − 1 = 0.1925, r o 19 5

H w c cow w d much oul the follo ing in ome stream b w g e orth assumin a 12% dis ount r ?ate

$ d100 received to ay.

$200 received r .1 yea from today

$400 received 2 .years from today

$300 received 3 .years from today

Question #55 of 87 Q IDuestion : 485756

Question #56 of 87 Q ID 76uestion : 412 1

$7 12 .32.

$810. .98

$1,112.44.

Explanation

N i FV PV

0 12 100 100.00

1 12 200 178.57

2 12 400 318.88

3 12 300 213. 35

810.98

Tom ill eti w r re 20 years from today an hasd $34,346 7. 4 rin his etirement account. He belie esv he ill w need $40,000 at the

b ge inning of each year r w dfor 20 years of etirement, with the first ithdr wa al on the ay he r . etires Tom assumes his investment

account ill w r %. d b g r d eturn 7 The amount he needs to eposit at the eginnin of this yea an each of the next 19 years is closest

to:

$7,300.

$7,800.

$6 5, 00.

Explanation

S c ctep 1: Cal ulate the amount needed r cat etirement at t = 20, with al ulator GN .in B mode

N = 20; FV = 0; I/Y = 7; PMT V = 40,000; CPT P = -453,423.81

Step 2: Calculate the required deposits at t = 0 to 19 to r 4esult in a time 20 value of 53,423.81. Remain in mo so that BGN de

the is in to one io afte the final ment FV dexed per d r pay .

PV = -34,346.74; N = 20; I/Y = 7; FV = 4 = -$53,423. P81; C T PMT 7,306.77

s the num of om oun in io in eases hat is the effe on the annual enta ate ber c p d g per ds cr , w ct perc ge r (APR c v) and the effe ti e

annual ate r (EAR ?)

APR E increases, AR remains the same.

APR increases, EAR incr .eases

Explanation

The APR remains the same since the APR c d ( pis ompute as interest er period) × (number c .of ompounding periods in 1 year)

Question #57 of 87 Q IDuestion : 412824

Question #58 of 87 Q IDuestion : 412830

Question #59 of 87 Q ID 796uestion : 412

s the of om oun in in eases the inte est ate io eases lea in the i inal frequency c p d g cr , r r per per d decr v g or g APR unchanged.

H w vo e er, Ethe AR w cincreases ith the frequency of ompounding.

N kki i Ali an onal to hel finan thei in an tion he annual ment loan ies d D d Ankard borrowed $15,000 p ce r wedd g d recep . T pay carr

a term of se env years an and 11 inte est ate es% r r . R pe acti el thev y, amount of the fi str p yment that is inte estr an thed amount

of the se on ment that is in i al c d pay pr c p a er approximately:

$ $1,650; 1,4 .68

$1,650; $1,702.

$1,468; $1,702.

Explanation

S ep C cu he ymet 1: al late t annual pa nt.

U c csing a finan ial cal ulator (remember c r Pto lea your registers): V = = 0; 15,000; FV I/Y = 11; N = 7; PMT 18 = $3, 3

S ep C cu he he yme eret 2: al late t portion of t first pa nt that is int st.

Inte er st = Pr × incipal Int st at 15 11) 65e er r e = ( ,000 × 0. = 1, 0

S ep C cu he he ec yme pr ct 3: al late t portion of t s ond pa nt that is in ipal.

Pr c r , , r c rin ipal = P − ayment Inte est = 3,183 − 1 650 = 1 533 (inte est cal ulation is f om Step 2)

Int in al Int st at 15 11 81e er st = Pr cip remaining × ere r e = [( ,000 − 1.533) × 0. ] = 1,4

Pr ,4 , 02incipal = P − ayment Interest = 3,183 − 1 81 = 1 7

Ma it s to ai in fo al ann al nts at an int st at of int st ntrc Schm z borrow $20,000 b pe d back ur equ u payme e er r e 8%. The e er a om u

in s on s nt l : the ec d year' payme wou d be

$1116 9. 0.

$6038.40.

$1244. 0.9

Explanation

With PV = 20,000, N = 4, I/Y = 8, computed Pmt = 6,038.42. Interest 1) 8) (Yr = 20,000(0.0 = 16 Int st00. ere (Yr2) = (20,000 −

(603 00 (0.0 244. 38.42 − 16 )) 8) = 1 9

1 1

2 1

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Test ID: 7658669 The Time Value of Money Question #1 of 87 Question ID: 412807
You borrow $15,000 to buy a car. The loan is to be paid off in monthly payments over 5 years at 12% annual interest. What is the amount of each payment? $456. $546. $334. Explanation I = 12 / 1 2 = 1
; N = 5 × 12 = 60; PV = 15,000; CPT → PMT = 333.67. Question #2 of 87 Question ID: 412753
Wei Zhang has funds on deposit with Iron Range bank. The funds are currently earning 6% interest. If he withdraws $15,000
to purchase an automobile, the 6% interest rate can be best thought of as a(n): discount rate. opportunity cost. financing cost. Explanation
Since Wei will be foregoing interest on the withdrawn funds, the 6% interest can be best characterized as an opportunity cost -
the return he could earn by postponing his auto purchase until the future. Question ID: 412768
A local bank offers an account that pays 8%, compounded quarterly, for any deposits of $10,000 or more that are left in the
account for a period of 5 years. The effective annual rate of interest on this account is: 8.24%. 4.65%. 9.01%. Explanation (1 + ) m − 1 = (1.02) 4 − 1 = 8.24%. Question #4 of 87 Question ID: 412759 A s the number of
, what is the effect on the EAR? EAR:
increases at a decreasing rate.
increases at an increasing rate. does not increase. Explanation
There is an upper limit to the EAR as the frequency of compounding increases. In the limit, with continuous compounding the EAR = eAP
R -1. Hence, the EAR increases at a decreasing rate. Question #5 of 87 Question ID: 412810 A n investor
s $4,000 in an account that pays 7.5%, compounded annually. How much will this investment be worth after 12 years? $5,850. $9,358. $9,527. Explanation
N = 12; I/Y = 7.5; PV = -4,000; PMT = 0; CPT → FV = $9,527. Question #6 of 87 Question ID: 412802
Consider a 10-year annuity that promises to pay out $10,000 per year; given this is an ordinary annuity and that an investor
can earn 10% on her money, the future value of this annuity, at the end of 10 years, would be: $159,374. $175,312. $110.000. Explanation
N = 10; I/Y = 10; PMT = -10,000; PV = 0; CPT → FV = $159,374. Question #7 of 87 Question ID: 412814
If 10 equal annual deposits of $1,000 are made into an investment account earning 9% starting today, how much will you have in 20 years? $39,204. $42,165. $35,967. Explanation
Switch to BGN mode. PMT = -1,000; N = 10, I/Y = 9, PV = 0; CPT → FV = 16,560.29. Remember the answer will be one year
after the last payment in annuity due FV problems. Now PV = 16,560.29; N = 10; I/Y = 9; PMT = 0; CPT → FV = 39,204.23. 10 Switch back to END mode. Question #8 of 87 Question ID: 412790
A n investor purchases a 10-year, $1,000 par value bond that pays annual coupons of $100. If the market rate of interest is 12%, what is the market value of the bond? $1,124. $950. Explanation
Note that bond problems are just mixed annuity problems. You can solve bond problems directly with your financial calculator
using all five of the main TVM keys at once. For bond-types of problems the bond's price (PV) will be negative, while the
coupon payment (PMT) and par value (FV) will be positive. N = 10; I/Y = 12; FV = 1,000; PMT = 100; CPT → PV = -886.99. Question #9 of 87 Question ID: 412773
Given: $1,000 investment, compounded monthly at 12% find the future value after one year. $1,121.35. $1,126.83. $1,120.00. Explanation
Divide the interest rate by the number of compound periods and multiply the number of years by the number of compound
periods. I = 12 / 12 = 1; N = (1)(12) = 12; PV = 1,000. Question #10 of 87 Question ID: 412785
A n investor deposits $10,000 in a bank account paying 5% interest compounded annually. Rounded to the nearest dollar, in 5 years the investor will have: $12,500. $10,210. Explanation
PV = 10,000; I/Y = 5; N = 5; CPT → FV = 12,763. or: 10,000(1.05)5 = 12,763. Question #11 of 87 Question ID: 412809
Given the following cash flow stream: End of Year Annual Cash Flow 1 $4,000 2 $2,000 3 -0- 4 -$1,000
Using a 10% discount rate, the present value of this cash flow stream is: $4,606. $3,415. $3,636. Explanation
PV(1): N = 1; I/Y = 10; FV = -4,000; PMT = 0; CPT → PV = 3,636
PV(2): N = 2; I/Y = 10; FV = -2,000; PMT = 0; CPT → PV = 1,653 PV(3): 0
PV(4): N = 4; I/Y = 10; FV = 1,000; PMT = 0; CPT → PV = -683
Total PV = 3,636 + 1,653 + 0 − 683 = 4,606 Question #12 of 87 Question ID: 412769
If a $45,000 car loan is financed at 12% over 4 years, what is the monthly car payment? $1,185. $985. $1,565. Explanation
N = 4 × 12 = 48; I/Y = 12/12 = 1; PV = -45,000; FV = 0; CPT → PMT = 1,185.02 Question #13 of 87 Question ID: 412786
Find the future value of the following uneven cash flow stream. Assume end of the year payments. The discount rate is 12%. Year 1 -2,000 Year 2 -3,000 Year 3 6,000 Year 4 25,000 Year 5 30,000 $33,004.15. $58,164.58. $65,144.33. Explanation
N = 4; I/Y = 12; PMT = 0; PV = -2,000; CPT → FV = -3,147.04
N = 3; I/Y = 12; PMT = 0; PV = -3,000; CPT → FV = -4,214.78
N = 2; I/Y = 12; PMT = 0; PV = 6,000; CPT → FV = 7,526.40
N = 1; I/Y = 12; PMT = 0; PV = 25,000; CPT → FV = 28,000.00
N = 0; I/Y = 12; PMT = 0; PV = 30,000; CPT → FV = 30,000.00
Sum the cash flows: $58,164.58.
A lternative calculation solution: -2,000 × 1.124 − 3,000 × 1.123 + 6,000 × 1.122 + 25,000 × 1.12 + 30,000 = $58,164.58. Question #14 of 87 Question ID: 412782
If $10,000 is invested in a mutual fund that returns 12% per year, after 30 years the investment will be worth: $300,000. $10,120. $299,599. Explanation FV = 10,000(1.12)3 0 = 299,599
Using TI BAII Plus: N = 30; I/Y = 12; PV = -10,000; CPT → FV = 299,599. Question #15 of 87 Question ID: 412811
A n annuity will pay eight annual
of $100, with the first payment to be received one year from now. If the interest rate
is 12% per year, what is the present value of this annuity? $1,229.97. $556.38. $496.76. Explanation
N = 8; I/Y = 12%; PMT = -$100; FV = 0; CPT → PV = $496.76. Question #16 of 87 Question ID: 412794
A ssuming a discount rate of 10%, which stream of annual payments has the highest present value? $20 -$5 $20 $110 -$100 -$100 -$100 $500 $110 $20 $10 $5 Explanation
This is an intuition question. The two cash flow streams that contain the $110 payment have the same total cash flow but the correct
answer is the one where the $110 occurs earlier. The cash flow stream that has the $500 that occurs four years hence is overwhelmed by
the large negative flows that precede it. Question #17 of 87 Question ID: 412756
The real risk-free rate can be thought of as:
approximately the nominal risk-free rate plus the expected inflation rate.
exactly the nominal risk-free rate reduced by the expected inflation rate. Explanation
The approximate relationship between nominal rates, real rates and expected inflation rates can be written as:
Nominal risk-free rate = real risk-free rate + expected inflation rate.
Therefore we can rewrite this equation in terms of the real risk-free rate as:
Real risk-free rate = Nominal risk-free rate - expected inflation rate
The exact relation is: (1 + real)(1 + expected inflation) = (1 + nominal) Question #18 of 87 Question ID: 412828
A n investor who requires an annual return of 12% has the choice of receiving one of the following:
A. 10 annual payments of $1,225.00 to begin at the end of one year.
B. 10 annual payments of $1,097.96 beginning immediately.
Which option has the highest present value (PV) and approximately how much greater is it than the other option?
Option B's PV is $114 greater than option A's.
Option B's PV is $27 greater than option A's.
Option A's PV is $42 greater than option B's. Explanation
Option A: N = 10, PMT = -$1,225, I = 12%, FV = 0, Compute PV = $6,921.52.
Option B: N = 9, PMT = -$1,097.96, I = 12%, FV = 0, Compute PV → $5,850.51 + 1,097.96 = 6,948.17 or put calculator in
Begin mode N = 10, PMT = $1,097.96, I = 12%, FV = 0, Compute PV → $6,948.17. Difference between the 2 options =
$6,921.52 − $6,948.17 = -$26.65.
Option B's PV is approximately $27 higher than option A's PV. Question #19 of 87 Question ID: 412778
A local bank offers a certificate of deposit (CD) that earns 5.0% compounded quarterly for three and one half years. If a
depositor places $5,000 on deposit, what will be the value of the account at maturity? $5,931.06. $5,949.77. $5,875.00. Explanation
The value of the account at maturity will be: $5,000 × (1 + 0.05 / 4)(3.5 × 4 )= $5.949.77;
or with a financial calculator: N = 3 years × 4 quarters/year + 2 = 14 periods; I = 5% / 4 quarters/year = 1.25; PV = $5,000;
PMT = 0; CPT → FV = $5,949.77. Question #20 of 87 Question ID: 412803
Justin Banks just won the lottery and is trying to decide between the annual cash flow payment option or the lump sum option.
He can earn 8% at the bank and the annual cash flow option is $100,000/year, beginning today for 15 years. What is the
annual cash flow option worth to Banks today? $855,947.87. $924,423.70. $1,080,000.00. Explanation
First put your calculator in the BGN.
N = 15; I/Y = 8; PMT = 100,000; CPT → PV = 924,423.70.
A lternatively, do not set your calculator to BGN, simply multiply the ordinary annuity (end of the period payments) answer by 1
+ I/Y. You get the annuity due answer and you don't run the risk of forgetting to reset your calculator back to the end of the period setting.
OR N = 14; I/Y = 8; PMT = 100,000; CPT → PV = 824,423.70 + 100,000 = 924,423.70. Question #21 of 87 Question ID: 412793
The following stream of cash flows will occur at the end of the next five years. Yr 1 -2,000 Yr 2 -3,000 Yr 3 6,000 Yr 4 25,000 Yr 5 30,000
A t a discount rate of 12%, the present value of this cash flow stream is closest to: $33,004. $58,165. $36,965. Explanation
N = 1; I/Y = 12; PMT = 0; FV = -2,000; CPT → PV = -1,785.71.
N = 2; I/Y = 12; PMT = 0; FV = -3,000; CPT → PV = -2,391.58.
N = 3; I/Y = 12; PMT = 0; FV = 6,000; CPT → PV = 4,270.68.
N = 4; I/Y = 12; PMT = 0; FV = 25,000; CPT → PV = 15,887.95.
N = 5; I/Y = 12; PMT = 0; FV = 30,000; CPT → PV = 17,022.81.
Sum the cash flows: $33,004.15.
Note: If you want to use your calculator's NPV function to solve this problem, you need to enter zero as the initial cash flow
(CF ). If you enter -2,000 as CF , all your cash flows will be one period too soon and you will get one of the wrong answers. 0 0 Question #22 of 87 Question ID: 485754
Paul Kohler inherits $50,000 and deposits it immediately in a bank account that pays 6% interest. No other deposits or
withdrawals are made. In two years, what will be the account balance assuming monthly compounding? $53,100. $50,500. $56,400. Explanation
To compound monthly, remember to divide the interest rate by 12 (6%/12 = 0.50%) and the number of periods will be 2 years
times 12 months (2 × 12 = 24 periods). The value after 24 periods is $50,000 × 1.00524 = $56,357.99.
The problem can also be solved using the time value of money functions: N = 24; I/Y = 0.5; PMT = 0; PV = 50,000; CPT FV = $56,357.99. Question ID: 412812
A n annuity will pay eight annual payments of $100, with the first payment to be received three years from now. If the interest
rate is 12% per year, what is the present value of this annuity? The present value of:
a lump sum discounted for 2 years, where the lump sum is the present value of
an ordinary annuity of 8 periods at 12%. a lump sum discounted for 3 y
ears, where the lump sum is the present value of an
ordinary annuity of 8 periods at 12%.
an ordinary annuity of 8 periods at 12%. Explanation
The PV of an ordinary annuity (calculation END mode) gives the value of the payments one period before the first payment,
which is a time = 2 value here. To get a time = 0 value, this value must be discounted for two periods (years). Question #24 of 87 Question ID: 412787
What is the maximum an investor should be willing to pay for an annuity that will pay out $10,000 at the beginning of each of the next 10
years, given the investor wants to earn 12.5%, compounded annually? $62,285. $52,285. $55,364. Explanation
Using END mode, the PV of this annuity due is $10,000 plus the present value of a 9-year ordinary annuity: N=9; I/Y=12.5;
PMT=-10,000; FV=0; CPT PV=$52,285; $52,285 + $10,000 = $62,285.
Or set your calculator to BGN mode then N=10; I/Y=12.5; PMT=-10,000; FV=0; CPT PV= $62,285. Question #25 of 87 Question ID: 412799
What is the present value of a 10-year, $100 annual annuity due if interest rates are 0%? No solution. $1,000. $900. Explanation
When I/Y = 0 you just sum up the numbers since there is no interest earned. Question #26 of 87 Question ID: 412792
If $2,000 a year is invested at the end of each of the next 45 years in a retirement account yielding 8.5%, how much will an
investor have at retirement 45 years from today? $100,135. $901,060. $90,106. Explanation
N = 45; PMT = -2,000; PV = 0; I/Y = 8.5%; CPT → FV = $901,060.79. Question #27 of 87 Question ID: 412755
Vega research has been conducting investor polls for Third State Bank. They have found the most investors are not willing to
tie up their money in a 1-year (2-year) CD unless they receive at least 1.0% (1.5%) more than they would on an ordinary
savings account. If the savings account rate is 3%, and the bank wants to raise funds with 2-year CDs, the yield must be at least: 4.5%, and this represents a r equired rate of return.
4.0%, and this represents a required rate of return.
4.5%, and this represents a discount rate. Explanation
Since we are taking the view of the minimum amount required to induce investors to lend funds to the bank, this is best
described as a required rate of return. Based upon the numerical information, the rate must be 4.5% (= 3.0 + 1.5). Question #28 of 87 Question ID: 412754
Selmer Jones has just inherited some money and wants to set some of it aside for a vacation in Hawaii one year from today.
His bank will pay him 5% interest on any funds he deposits. In order to determine how much of the money must be set aside
and held for the trip, he should use the 5% as a: discount rate. required rate of return. opportunity cost. Explanation
He needs to figure out how much the trip will cost in one year, and use the 5% as a discount rate to convert the future cost to a
present value. Thus, in this context the rate is best viewed as a discount rate. Question #29 of 87 Question ID: 412770 Jamie Morgan needs to
$2,000 in 18 months. If she can earn 6% at the bank, quarterly, how much must she deposit today? $1,829.08. $1,832.61. $1,840.45. Explanation
Each quarter of a year is comprised of 3 months thus N = 18 / 3 = 6; I/Y = 6 / 4 = 1.5; PMT = 0; FV = 2,000; CPT → PV = $1,829.08. Question #30 of 87 Question ID: 412816
Renee Fisher invests $2,000 each year, starting one year from now, in a retirement account. If the investments earn 8% or
10% annually over 30 years, the amount Fisher will accumulate is closest to: 8% 10% $245,000 $360,000 $225,000 $330,000 $225,000 $360,000 Explanation
N = 30; I/Y = 8; PMT = -2,000; PV = 0; CPT FV = 226,566.42
N = 30; I/Y = 10; PMT = -2,000; PV = 0; CPT FV = 328,988.05 Question #31 of 87 Question ID: 412829
It will cost $20,000 a year for four years when an 8-year old child is ready for college. How much should be invested today if
the child will make the first of four annual withdrawals 10-years from today? The expected rate of return is 8%. $66,243. $30,683. $33,138. Explanation
First, find the present value of the college costs as of the end of year 9. (Remember that the PV of an ordinary annuity is as of
time = 0. If the first payment is in year 10, then the present value of the annuity is indexed to the end of year 9). N = 4; I/Y = 8;
PMT = 20,000; CPT → PV = $66,242.54. Second, find the present value of this single sum: N = 9; I/Y = 8; FV = 66,242.54;
PMT = 0; CPT → PV = 33,137.76. Question #32 of 87 Question ID: 485755
A n investor makes 48 monthly payments of $500 each beginning today into an account that will have a value of $29,000 at the
end of four years. The stated annual interest rate is closest to: 9.50%. 9.00%. 10.00%. Explanation
Because this is an annuity due (payments at the start of each period) the calculator must first be set to BGN mode.
N = 48; PMT = 500; FV = -29,000; PV = 0; CPT I/Y = 0.7532
This percentage is a monthly rate because the time periods were entered as 48 months. It must be converted to a stated
annual percentage rate (APR) by multiplying by the number of compounding periods per year: 0.7532 × 12 = 9.04%. Question #33 of 87 Question ID: 434184
A stated interest rate of 9% compounded semiannually results in an effective annual rate closest to: 9.3%. 9.1%. 9.2%. Explanation
Semiannual rate = 0.09 / 2 = 0.045.
Effective annual rate = (1 + 0.045) 2 − 1 = 0.09203, or 9.203%. Question #34 of 87 Question ID: 412760
A local bank advertises that it will pay interest at the rate of 4.5%, compounded monthly, on regular savings accounts. What is
the effective rate of interest that the bank is paying on these accounts? 4.59%. 4.50%. 4.65%. Explanation (1 + 0.045 / 12)1
2 − 1 = 1.0459 − 1 = 0.0459. Question #35 of 87 Question ID: 412822
Sarah Parker is buying a new $25,000 car. Her trade-in is worth $5,000 so she needs to borrow $20,000. The loan will be paid
in 48 monthly installments and the annual interest rate on the loan is 7.5%. If the first payment is due at the end of the first
month, what is Sarah's monthly car payment? $480.57. $483.58. $416.67. Explanation
N = 48; I/Y = 7.5 / 12 = 0.625; PV = 20,000; FV = 0; CPT → PMT = 483.58. Question #36 of 87 Question ID: 412808
A n investment offers $100 per year forever. If Peter Wallace's required rate of return on this investment is 10%, how much is this investment worth to him? $1,000. $10,000. $500. Explanation
For a perpetuity, PV = PMT ÷ I = 100 ÷ 0.10 = 1 ,000. Question #37 of 87 Question ID: 412823
How much should an investor have in a retirement account on his 65t
h birthday if he wishes to withdraw $40,000 on that
birthday and each of the following 14 birthdays, assuming his retirement account is expected to earn 14.5%? $274,422. $272,977. $234,422. Explanation
This is an annuity due so set your calculator to the BGN mode. N = 15; I/Y = 14.5; PMT = -40,000; FV = 0; CPT → PV =
274,422.50. Switch back to END mode. Question #38 of 87 Question ID: 412806
What is the present value of a 12-year annuity due that pays $5,000 per year, given a discount rate of 7.5%? $36,577. $41,577. $38,676. Explanation
Using your calculator: N = 11; I/Y = 7.5; PMT = -5,000; FV = 0; CPT → PV = 36,577 + 5,000 = $41,577. Or set your calculator
to BGN mode and N = 12; I/Y = 7.5; PMT = -5,000; FV = 0; CPT → PV = $41,577. Question ID: 412804
Concerning an ordinary annuity and an annuity due with the same payments and positive interest rate, which of the following statements is most accurate? There is no relationship.
The present value of the ordinary annuity is less than an annuity due.
The present value of the ordinary annuity is greater than an annuity due. Explanation
With a positive interest rate, the present value of an ordinary annuity is less than the present value of an annuity due. The first
cash flow in an annuity due is at the beginning of the period, while in an ordinary annuity, the first cash flow occurs at the end
of the period. Therefore, each cash flow of the ordinary annuity is discounted one period more. Question #43 of 87 Question ID: 412801
If $2,500 were put into an account at the end of each of the next 10 years earning 15% annual interest, how much would be in
the account at the end of ten years? $27,461. $41,965. $50,759. Explanation
N = 10; I = 15; PMT = 2,500; CPT → FV = $50,759. Question #44 of 87 Question ID: 412825
Elise Corrs, hedge fund manager and avid downhill skier, was recently granted permission to take a 4 month sabbatical.
During the sabbatical, (scheduled to start in 11 months), Corrs will ski at approximately 12 resorts located in the Austrian,
Italian, and Swiss Alps. Corrs estimates that she will need $6,000 at the beginning of each month for expenses that month.
(She has already financed her initial travel and equipment costs.) Her financial planner estimates that she will earn an annual
rate of 8.5% during her savings period and an annual rate of return during her sabbatical of 9.5%. How much does she need
to put in her savings account at the end of each month for the next 11 months to ensure the cash flow she needs over her
sabbatical? Each month, Corrs should save approximately: $2,070. $2,080. $2,065. Explanation
This is a two-step problem. First, we need to calculate the present value of the amount she needs over her sabbatical. (This
amount will be in the form of an annuity due since she requires the payment at the beginning of the month.) Then, we wil use
future value formulas to determine how much she needs to save each month.
Step 1: Calculate present value of amount required during the sabbatical
Using a financial calculator: Set to BEGIN Mode, then N = 4; I/Y = 9.5 / 12 = 0.79167; PMT = 6,000; FV = 0; CPT → PV = -23,719.
Step 2: Calculate amount to save each month
Using a financial calculator: Make sure it is set to END mode, then N = 11; I/Y = 8.5 / 12.0 = 0.70833; PV = 0; FV = 23,719;
CPT → PMT= -2,081, or approximately $2,080. Question #45 of 87 Question ID: 412797
Compute the present value of a perpetuity with $100 payments beginning four years from now. Assume the appropriate annual interest rate is 10%. $1000. $751. $683. Explanation
Compute the present value of the perpetuity at (t = 3). Recall, the present value of a perpetuity or annuity is valued one period
before the first payment. So, the present value at t = 3 is 100 / 0.10 = 1,000. Now it is necessary to discount this lump sum to t
= 0. Therefore, present value at t = 0 is 1,000 / (1.10) 3 = 751. Question #46 of 87 Question ID: 412772
What is the maximum price an investor should be willing to pay (today) for a 10 year annuity that will generate $500 per
quarter (such payments to be made at the end of each quarter), given he wants to earn 12%, compounded quarterly? $11,557. $6,440. $11,300. Explanation
Using a financial calculator: N = 10 × 4 = 40; I/Y = 12 / 4 = 3; PMT = -500; FV = 0; CPT → PV = 11,557. Question #47 of 87 Question ID: 412757
T-bill yields can be thought of as:
real risk-free rates because they contain an inflation premium.
nominal risk-free rates because they do not contain an inflation premium.
nominal risk-free rates because they contain an inflation premium. Explanation
T-bills are government issued securities and are therefore considered to be default risk free. More precisely, they are nominal
risk-free rates rather than real risk-free rates since they contain a premium for expected inflation. Question #48 of 87 Question ID: 412780
A certain investment product promises to pay $25,458 at the end of 9 years. If an investor feels this investment should
produce a rate of return of 14%, compounded annually, what's the most he should be willing to pay for it? $7,829. $9,426. $7,618. Explanation
N = 9; I/Y = 14; FV = -25,458; PMT = 0; CPT → PV = $7,828.54. or: 25,458/1.14 9 = 7,828.54 Question #49 of 87 Question ID: 412813
If an investor puts $5,724 per year, starting at the end of the first year, in an account earning 8% and ends up accumulating
$500,000, how many years did it take the investor? 27 years. 87 years. 26 years. Explanation
I/Y = 8; PMT = -5,724; FV = 500,000; CPT → N = 27.
Remember, you must put the pmt in as a negative (cash out) and the FV in as a positive (cash in) to compute either N or I/Y. Question #50 of 87 Question ID: 412800
A n investor will receive an annuity of $5,000 a year for seven years. The first payment is to be received 5 years from today. If
the annual interest rate is 11.5%, what is the present value of the annuity? $13,453. $23,185. $15,000. Explanation With PMT = 5,000; N = 7
; I/Y = 11.5; value (at t = 4) = 23,185.175. Therefore, PV (at t = 0) = 23,185.175 / (1.115) 4 = $15,000.68. Question #51 of 87 Question ID: 412765
What's the effective rate of return on an investment that generates a return of 12%, compounded quarterly? 12.00%. 14.34%. 12.55%. Explanation (1 + 0.12 / 4)
4 − 1 = 1.1255 − 1 = 0.1255. Question #52 of 87 Question ID: 412776
In 10 years, what is the value of $100 invested today at an interest rate of 8% per year, compounded monthly? $222. $216. $180. Explanation
N = 10 × 12 = 120; I/Y = 8/12 = 0.666667; PV = -100; PMT = 0; CPT → FV = 221.96. Question #53 of 87 Question ID: 485753
If an investment has an APR of 18% and is compounded quarterly, its effective annual rate (EAR) is closest to: 18.00%. 19.25%. 18.81%. Explanation
Because this investment is compounded quarterly, we need to divide the APR by four compounding periods: 18 / 4 = 4.5%.
EAR = (1.045)4 − 1 = 0.1925, or 19.25%. Question #54 of 87 Question ID: 412805
How much would the following income stream be worth assuming a 12% discount rate? $100 received today.
$200 received 1 year from today.
$400 received 2 years from today.
$300 received 3 years from today. $721.32. $810.98. $1,112.44. Explanation N i FV PV 0 12 100 100.00 1 12 200 178.57 2 12 400 318.88 3 12 300 213.53 810.98 Question #55 of 87 Question ID: 485756
Tom will retire 20 years from today and has $34,346.74 in his retirement account. He believes he will need $40,000 at the
beginning of each year for 20 years of retirement, with the first withdrawal on the day he retires. Tom assumes his investment
account will return 7%. The amount he needs to deposit at the beginning of this year and each of the next 19 years is closest to: $7,300. $7,800. $6,500. Explanation
Step 1: Calculate the amount needed at retirement at t = 20, with calculator in BGN mode.
N = 20; FV = 0; I/Y = 7; PMT = 40,000; CPT PV = -453,423.81
Step 2: Calculate the required deposits at t = 0 to 19 to result in a time 20 value of 453,423.81. Remain in BGN mode so that
the FV is indexed to one period after the final payment.
PV = -34,346.74; N = 20; I/Y = 7; FV = 453,423.81; CPT PMT = -$7,306.77 Question #56 of 87 Question ID: 412761
A s the number of compounding periods increases, what is the effect on the annual percentage rate (APR) and the effective annual rate (EAR)?
APR increases, EAR remains the same. APR increases, EAR increases. Explanation
The APR remains the same since the APR is computed as (interest per period) × (number of compounding periods in 1 year).
A s the frequency of compounding increases, the interest rate per period decreases leaving the original APR unchanged.
However, the EAR increases with the frequency of compounding. Question #57 of 87 Question ID: 412824
Nikki Ali and Donald Ankard borrowed $15,000 to help finance their wedding and reception. The annual payment loan carries
a term of seven years and an 11% interest rate. Respectively, the amount of the first payment that is interest and the amount
of the second payment that is principal are approximately: $1,650; $1,468. $1,650; $1,702. $1,468; $1,702. Explanation
Step 1: Calculate the annual payment.
Using a financial calculator (remember to clear your registers): PV = 15,000; FV = 0; I/Y = 11; N = 7; PMT = $3,183
Step 2: Calculate the portion of the first payment that is interest.
Interest = Principal × Interest rate = (15,000 × 0.11) = 1,650 1
Step 3: Calculate the portion of the second payment that is principal.
Principal1 = Payment − Interest1 = 3,183 − 1,650 = 1,533 (interest calculation is from Step 2) Interest 2 = Principal remaining × I
nterest rate = [(15,000 − 1.533) × 0.11] = 1,481
Principal2 = Payment − Interest1 = 3,183 − 1,481 = 1,702 Question #58 of 87 Question ID: 412830
Marc Schmitz borrows $20,000 to be paid back in four equal annual payments at an interest rate of 8%. The interest amount
in the second year's payment would be: $1116.90. $6038.40. $1244.90. Explanation
With PV = 20,000, N = 4, I/Y = 8, computed Pmt = 6,038.42. Interest (Yr1) = 20,000(0.08) = 1600. Interest (Yr2) = (20,000 −
(6038.42 − 1600))(0.08) = 1244.93 Question #59 of 87 Question ID: 412796