Finance Problems P5-4
Future Values: For each of the cases shown in the following table, calculate the future value of the single cash flow deposited today at the end of the deposit period if the interest is compounded annually at the rate specified.
|
Case
|
Single cash flow
|
Interest rate
|
Deposit period (years)
|
|
A
|
$200
|
5%
|
20
|
|
B
|
$4,500
|
8%
|
7
|
|
C
|
$10,000
|
9%
|
10
|
|
D
|
$25,000
|
10%
|
12
|
|
E
|
$37,000
|
11%
|
5
|
|
f
|
$40,000
|
12%
|
9
|
P5-5 Time Value: You have $1,500 to invest today at 7% interest compounded annually.
A. Find out how much you will have accumulated in the account at the end of (1) 3 years (2) 6 years and (3) 9 years.
B. Use your findings in part A to calculate the amount of interest earned in (1) the first 3 years (years 1 to 3), (2) the second 3 years (years 4 to 6), and (3) the third 3 years (years 7 to 9).
C. Compare and contrast your findings in part B. Explain why the amount of interest earned increases in each succeeding 3 year period?
P5-7 Time Value: You can deposit $10,000 into an account paying 9% annual interest either today or exactly ten years from today. How much better off will you be at the end of 40 years if you decide to make the initial deposit today rather than 10 years from today?
P5-13 Time Value: Jim Nance has been offered an investment that will pay him $500 three years from now.
A. If his opportunity cost is 7% compounded annually, what value should he place on this opportunity today?
B. What is the most he should pay to purchase this payment today?
C. If Jim can purchase this investment for less than the amount calculated in part A, what does that imply about the rate of return that he will earn on the investment?
P5-16 Time value comparisons of single amounts: In exchange for a $20,000 payment today, a well-known company will allow you to choose one of the alternatives shown in the following table. Your opportunity cost is 11%.
|
Alternative
|
Single amount
|
|
A
|
$28,500 at end of 3 years
|
|
B
|
$54,000 at end of 9 years
|
|
C
|
$160,000 at end of 20 years
|
a. Find the value today of each alternative.
b. Are all the alternatives acceptable-that is, worth $20,000 today?
c. Which alternative, if any, will you take?
P5-20 Present Value of an annuity: Consider the following cases:
|
Case
|
Amount of annuity
|
Interest rate
|
Period (years)
|
|
A
|
$12,000
|
7%
|
3
|
|
B
|
$55,000
|
12%
|
15
|
|
C
|
$700
|
20%
|
9
|
|
D
|
$140,000
|
5%
|
7
|
|
e
|
$22,500
|
10%
|
5
|
a. Calculate the present value of the annuity assuming that it is (1.) an ordinary annuity (2) an annuity due.
b. Compare your findings in parts a (1) and a (2). All else being identical, which type of annuity- ordinary or annuity due is preferable? Explain why.
P5-21 Time Value: Annuities. Marian Kirk wishes to select the better of two 10 year annuities C and D. Annuity C is an ordinary annuity of $2,500 per year for 10 years. Annuity D is an annuity due of $2,200 per year for 10 years.
a. Find the future value of both annuities at the end of the year 10, assuming that Marian can earn (1) 10% annual interest and (2) 20% annual interest.
b. Use your findings in part a to indicate which annuity has the greater future value at the end of year 10 for both the (1) 10% and (2) 20% interest rates.
c. Find the present value of both annuities, assuming that Marian can earn (1) 10% annual interest and (2) 20% annual interest.
d. Use your findings in part c to indicate which annuity has the greater present value for both (1) 10%and (2) 20% annual interest rates.
e. Briefly compare, contrast, and explain any differences between your findings using the 10% and 20% interest rates in part b and part d.
P5-23 Value of a retirement annuity: An insurance agent is trying to sell you an immediate-retirement annuity, which for a single amount paid today, will provide you with $12,000 at the end of each year for the next 25 years. You currently earn 9% on low-risk investments comparable to the retirement annuity. Ignoring taxes, what is the most you would pay for this annuity?