Tài liệu tham khảo cháp 2 - Tài liệu tham khảo | Đại học Hoa Sen

Chapter 2 Future value
1. Gerold invested $5,500 in an account that pays 6.5% simple interest. How much money
will he have at the end of ten years?
2. David invested $10,900 in an account that pays 7.0% simple interest. How much money
will he have at the end of three years?
3. Gerold invested $5,500 in an account that pays 6.5% simple interest. How much money
will he have earned over a 10 – years period if the interest had compounded annually?
4. David invested $10,900 in an account that pays 7.0%. How much money will he have
earned over a 3 – years period if the interest had compounded annually?
5. Gerold invested $5,500 in an account that pays 6.5% simple interest. How much more
could him have earned over a 10 – years period if the interest had compounded annually?
6. David invested $10,900 in an account that pays 7.0%. How much more could him have
earned over a 3 – years period if the interest had compounded annually?
7. What is the future value of $7.200 invested for 20 years at 8.8% compounded annually?
8. You have $6000 invested in a bank account. Suppose banks are currently paying an
interest rate of 9.2% per year on deposits. Calculate your earnings after 3 years, 4 years, 5 years, 10 years?
9. Suppose that Peter Minuit did not become the first New York real estate tycoon but
instead had invested his $24 at a 5% interest rate in New Amsterdam Savings Bank. What
would have been the balance in his account after 5 years? 50 years?
10. Jay Ritter invested $1,000 in the stock of the SDH Company. The company pays a current
dividend of $2, which is expected to grow by 20 percent per year for the next two years.
What will the dividend of the SDH Company be after two years?
11. You have $4000 invested in a bank account. Your bank account pays a 8% nominal rate
of interest. The interest is compounded quarterly. How much will you have at the end of 2 years?
12. If a person deposits $10,000 in the bank today, what will the money be worth in 3 years at
9% if it’s a compounded annually? (compounded semi – annually; compounded monthly, compounded quarterly)
13. Today, you earn an annual salary of $14,400. What will be your annual salary 10 years
from now if you earn annual raise of 5%?
14. You hope to buy a dream car three years from now. Today, this car costs $40,000. You
expect the price to increase by an average of 4% per year over the next 3 years. How
much will your dream car cost by the time you are ready to buy it?
15. You just received $ 150,000 from an insurance settlement. You have decided to set this
money aside and invest it for your retirement. Currently, your goal is to retire 20 years
from today. How much money will you have on your account on the day you retire if you
can earn an average return of 9%?
16. If a person deposits $11,500 in the bank today, what will the money be worth in 3 years at 8% if
17. it’s a.) compounded semi-annually; b.) compounded quarterly; and c.) compounded annually Present value
16. You want to begin saving for your daughter’s college education and you estimate that she
will need $120,000 in 18 years. If you feel confident that you can earn 7.5% per year,
how much do you need to invest today?
17. Your parents set up a trust fund for you 10 years ago that is now worth $15,017.10. If the
fund earned 6.5% per year, how much did your parents invest?
18. What is the present value of $9.000 to be received 5 years from today if the discount rate is 9.2%.
19. What is the present value of $500 to be received in 5 years? 10 years? The discount rate is 10%
20. Suppose you need $15,000 in 3 years. If you can earn 6% annually, how much do you need to invest today?
21. Calculate the present value of $8,000 to be received in 4 years at a discount rate of 7.5%
if it is compounded (annually / semi-annually / quarterly).
22. Calculate the present value of $20,000 to be received in 5 years at a discount rate of 8.2%
if it is compounded (annually / semi-annually / quarterly).
23. How much must a person put into the bank today if he wants $12,000 in 4 years at 8.4%
compounded annually, semi – annually?
Saving for a future purchase
24. Suppose you need $4,500 next 3 years to buy a new motorcycle. The interest rate is 9%
per year. How much money should you set aside now in order to pay for the purchase?
25. You have just received notification that you have won the $1.2 million first prize in the
Centennial Lottery. However, the prize will be awarded on your 70th birthday, 50 years
from now. The appropriate discount rate is 8.5 percent. What is the present value of your winnings?
Finding the interest rate
26. Three year ago, you invested $3,200. Today it is worth $3,898.2. What rate of interest did you earn?
27. Mark invested $1,500 two years ago and expected to have 2,200. He has not added or
withdrawn any money from this account since his initial investment. All interest was
reinvested in the account. As it turns out, Mark only has 2,000 in his count today.
Compute the interest rate are pays for this investment.
28. 40 year ago, your mother invested $5,000. Today that investment is worth $430,065.11.
What is the average annual rate of return she earned on this investment?
29. Fifteen years ago, Jackson Supply set aside $130,000 in case of a financial emergency.
30. Today, that account has increased in value to $330,592. What rate of interest is the firm 31. earning on this money?
29. Fifteen years ago, Jackson Supply set aside $130,000 in case of a financial emergency.
Today, that account has increased in value to $330,592. What rate of interest is the firm earning on this money?
30. Assume the total cost of a college education will be $300,000 when your child enters
college in 16 years. You presently have $75,561 to invest. What rate of interest must you
earn on your investment to cover the cost of your child's college education?
31. On your ninth birthday, you received $300 which you invested at 4.5 percent interest,
compounded annually. Your investment is now worth $756. How old are you today?
32. At 10 percent interest, how long would it take to triple your money?
33. You're trying to save to buy a new $160,000 Ferrari. You have $56,000 today that can be
invested at your bank. The bank pays 6 percent annual interest on its accounts. How
many years will it be before you have enough to buy the car? Assume the price of the car remains constant.
34. You expect to receive $9,000 at graduation in 2 years. You plan on investing this money
at 10 percent until you have $60,000. How many years will it be until this occurs Multiple Cash flow
Uneven cash flow - Future cash flow
35. What is the future value of the following cash flows at the end of year 3 if the interest
rate is 6%? The cash flows occur at the end of each year. Year 1 Year 2 Year 3 $5,180 $9,600 $2,250
36. Suzette is going to receive $10,000 today as the result of an insurance settlement. In
addition, she will receive $15,000 one year from today and $25,000 two years from
today. She plans on saving all of this money and investing it for her retirement. If Suzette
can earn an average of 11% on her investments, how much will she have in her account if
she retires 25 years from today?
37. What is the future value of the following cash flows at the end of year 3 if the interest
rate is 7.25%? The cash flows occur at the end of each year. Year 1 Year 2 Year 3 $6,800 $2,100 $0
38. What is the future value of the following cash flows at the end of year 3 if the interest
rate is 9%? The cash flows occur at the end of each year. Year 1 Year 2 Year 3 $9,820 $0 $4,510
39. The government has imposed a fine on the Not-So-Legal Company. The fine calls for
annual payments of $100,000, $250,000, and $250,000, respectively over the next three
years. The first payment is due one year from today. The government plans to invest the
funds until the final payment is collected and then donate the entire amount, including
investment earnings, to a national health center. The government will earn 3.5% on the
funds held. How much will the national health center receive three years from today?
Finding Present cashflow
40. You are considering a project with the following cash flows: Year 1 Year 2 Year 3 $1,200 $1,800 $2,900
What is the present value of these cash flows, given a 9% discount rate?
41. You are considering a project with the following cash flows: Year 1 Year 2 Year 3 $4,200 $5,000 $5,400
What is the present value of these cash flows, given a 3% discount rate?
42. You are considering two savings options. Both options offer a 4% rate of return. The first
option is to save $1,200, $1,500, and $2,000 a year over the next three years, respectively.
The other option is to save one lump sum amount today. If you want to have the same
balance in your savings at the end of the three years, regardless of the savings method
you select, how much do you need to save today if you select the lump sum option?
43. You are considering two insurance settlement offers. The first offer includes annual
payments of $5,000, $7,500, and $10,000 over the next three years, respectively. The
other offer is the payment of one lump sum amount today. You are trying to decide which
offer to accept given the fact that your discount rate is 5%. What is the minimum amount
that you will accept today if you are to select the lump sum offer?
44. You are considering a job offer. The job offers an annual salary of $52,000, $55,000, and
$60,000 a year for the next three years, respectively. The offer also includes a starting
bonus of $2,000 payable immediately. What is this offer worth to you today at a discount rate of 6%?
45. Your local travel agent is advertising an extravagant global vacation. The package deal
requires that you pay $5,000 today, $15,000 one year from today, and a final payment of
$25,000 on the day you leave two years from today. What is the cost of this vacation in
today’s dollars if the discount rate is 6%?
46. One year ago, the Jenkins Family Fun Center deposited $3,600 in an investment account
for the purpose of buying new equipment four years from today. Today, it is adding
another $5,000 to this account. It plans on making a final deposit of $7,500 to the account
next year. How much will be available when it is ready to buy the equipment, assuming it earns a 7% rate of return? Perpetuity Finding Present value
47. George Jefferson established a trust fund that provides $150,000 in scholarships each
year for worthy students. The trust fund earns a 4.25% rate of return. How much money
did Mr. Jefferson contribute to the fund assuming that only the interest income is distributed?
48. A 9% preferred stock pays an annual dividend of $4.50. What is one share of this stock worth today?
49. You would like to establish a trust fund that will provide $50,000 a year forever for your
heirs. The trust fund is going to be invested very conservatively so the expected rate of
return is only 2.75%. How much money must you deposit today to fund this gift for your heirs
50. You just paid $350,000 for a policy that will pay you and your heirs $12,000 a year
forever. What rate of return are you earning on this policy?
51. The Eternal Gift Insurance Company is offering you a policy that will pay you and your
heirs $10,000 a year forever. The cost of the policy is $285,000. What is the rate of return on this policy?
52. Your rich uncle establishes a trust in your name and deposits $150,000 in it. The trust
pays a guaranteed 4% rate of return. How much will you receive each year if the trust is
required to pay you all of the interest earnings on an annual basis?
53. The preferred stock of ABC Co. offers an 8.4% rate of return. The stock is currently
priced at $50.00 per share. What is the amount of the annual dividend? Ordinary Anuity Finding Present value
54. The Bluebird Company has a $10,000 liability it must pay three years from today.
55. The company is opening a savings account so that the entire amount will be available when this
56. debt needs to be paid. The plan is to make an initial deposit today and then deposit an additional
57. $2,500 a year for the next three years, starting one year from today. The account pays a 3% rate
58. of return. How much does the Bluebird Company need to deposit today?
54. Your parents are giving you $100 a month for four years while you are in college. At a
6% discount rate, what are these payments worth to you when you first start college?
55. You just won the lottery! As your prize you will receive $1,200 a month for 100 months.
If you can earn 8% on your money, what is this prize worth to you today?
56. Todd is able to pay $160 a month for five years for a car. If the interest rate is 4.9%, how
much can Todd afford to borrow to buy a car?
57. You are the beneficiary of a life insurance policy. The insurance company informs you
that you have two options for receiving the insurance proceeds. You can receive a lump
sum of $50,000 today or receive payments of $641 a month for ten years. You can earn
6.5% on your money. Which option should you take and why?
58. Your employer contributes $25 a week to your retirement plan. Assume that you work for
your employer for another twenty years and that the applicable discount rate is 5%. Given
these assumptions, what is this employee benefit worth to you today?
59. You have a sub-contracting job with a local manufacturing firm. Your agreement calls for
annual payments of $50,000 for the next five years. At a discount rate of 12%, what is this job worth to you today? Finding PMT
60. You retire at age 60 and expect to live another 27 years. On the day you retire, you have
$464,900 in your retirement savings account. You are conservative and expect to earn
4.5% on your money during your retirement. How much can you withdraw from your
retirement savings each month if you plan to die on the day you spend your last penny.
61. The McDonald Group purchased a piece of property for $1.2 million. It paid a down
payment of 20% in cash and financed the balance. The loan terms require monthly
payments for 15 years at an annual percentage rate of 7.75% compounded monthly. What
is the amount of each mortgage payment?
62. You estimate that you will have $24,500 in student loans by the time you graduate. The
interest rate is 6.5%. If you want to have this debt paid in full within five years, how much must you pay each month? Finding rate
63. The Robertson Firm is considering a project which costs $123,900 to undertake. The
project will yield cash flows of $4,894.35 monthly for 30 months. What is the rate of return on this project?
64. Your insurance agent is trying to sell you an annuity that costs $100,000 today. By buying
this annuity, your agent promises that you will receive payments of $384.40 a month for
the next 40years. What is the rate of return on this investment? Finding Future value
You retire at age 60 and expect to live another 27 years. On the day you retire, you have
$464,900 in your retirement savings account. You are conservative and expect to earn 4.5% on
your money during your retirement. How much can you withdraw from your retirement savings
each month if you plan to die on the day you spend your last penny
You retire at age 60 and expect to live another 27 years. On the day you retire, you have
$464,900 in your retirement savings account. You are conservative and expect to earn 4.5% on
your money during your retirement. How much can you withdraw from your retirement savings
each month if you plan to die on the day you spend your last penny
65. Janet plans on saving $3,000 a year and expects to earn 8.5%. How much will Janet have
at the end of twenty-five years if she earns what she expects?
66. What is the future value of $2,400 a year for three years at an 8% rate of interest? Finding Rate ordinary
67. You have been investing $120 a month for the last 15 years. Today, your investment
account is worth $47,341.19. What is your average rate of return on your investments?e. 9.46%
68. Brinker, Inc. has been investing $136,000 a year for the past 4 years into a business
venture. Today, Brinker sold that venture for $685,000. What is its rate of return on this venture?c. 15.59% Annuity due Finding Present value
69. Your great-aunt left you an inheritance in the form of a trust. The trust agreement states
that youare to receive $2,500 on the first day of each year, starting immediately and
continuing for fifty years. What is the value of this inheritance today if the applicable discount rate is 6.35%?
70. The Ajax Co. just decided to save $1,500 a month for the next five years as a safety net
for recessionary periods. The money will be set aside in a separate savings account which
pays 3.25% interest compounded monthly. It deposits the first $1,500 today. If the
company had wanted to deposit an equivalent lump sum today, how much would it have had to deposit?
71. You need some money today and the only friend you have that has any is your ‘miserly’
friend. He agrees to loan you the money you need, if you make payments of $20 a month
for the next six months. In keeping with his reputation, he requires that the first payment
be paid today. He also charges you 1.5% interest per month. How much money are you borrowing?
72. You buy an annuity which will pay you $12,000 a year for ten years. The payments are
paid on the first day of each year. What is the value of this annuity today at a 7% discount rate?
73. You are scheduled to receive annual payments of $10,000 for each of the next 25 years.
Your discount rate is 8.5%. What is the difference in the present value if you receive
these payments at the beginning of each year rather than at the end of each year?
74. You are comparing two annuities with equal present values. The applicable discount rate
is 7.5%. One annuity pays $5,000 on the first day of each year for twenty years. How
much does the second annuity pay each year for twenty years if it pays at the end of each year? Finding Time
75. The Bad Guys Co. is notoriously known as a slow-payer. It currently needs to borrow
$25,000 and only one company will even deal with Bad Guys. The terms of the loan call
for daily payments of $30.76. The first payment is due today. The interest rate is 21%
compounded daily.What is the time period of this loan?c. 3.00 years Rate Finding FV, PV
76. The Bluebird Company has a $10,000 liability it must pay three years from today. The
company is opening a savings account so that the entire amount will be available when
this debt needs to be paid. The plan is to make an initial deposit today and then deposit an
additional $2,500 a year for the next three years, starting one year from today. The
account pays a 3% rate of return. How much does the Bluebird Company need to deposit today? Finding PMT
77. Your firm wants to save $250,000 to buy some new equipment three years from now. The
plan is to set aside an equal amount of money on the first day of each year starting today.
The firm can earn a 4.7% rate of return. How much does the firm have to save each year to achieve its goal? Future value
78. Today is January 1. Starting today, Sam is going to contribute $140 on the first of each
month to his retirement account. His employer contributes an additional 50% of the
amount contributed by Sam. If both Sam and his employer continue to do this and Sam
can earn a monthly rate of ½ of 1 percent, how much will he have in his retirement account 35 years from now?