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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) 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.
Today, that account has increased in value to $330,592. What rate of interest is the firm earning on this money? 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 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%? 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? Ordinary Anuity Finding Present value
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? 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? 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?