University of Pennsylvania
The Wharton School
FNCE 100
A. Craig MacKinlay
PROBLEM SET #1
Fall Term 2005
Present Value and Term Structure
1. Given an annual interest rate of 10 percent, what is the present (
t
= 0) value of a
stream of $100 annual payments starting in one year and ending in 20 years?
2. An investment of $1,000 earns 8 percent interest per year for three years. A second
$1,000 investment earns 1 percent for the first and second years and 22 percent the
third year.
(a) What is the average (arithmetic) of the returns on each of the investments over
the three years?
(b) Compute the terminal value of each investment. Which is larger?
(c) What is the compound rate of interest at which the initial $1,000 rises to the
terminal value of each investment?
(d) What is the geometric mean of the returns on each project?
(e) How do your results in Part d compare with your results in Part c? Comment on
the implications.
3. You purchase a bond for $900 and are promised coupon payments of $50 per year for
the next 15 years and then a maturity payment of $1000. (The coupon payments come
at year end.) Your ordinary income is taxed at the 25 percent rate while your capital
gains are taxed at the 10 percent rate. What is the aftertax yield to maturity on this
investment?
Your capital gains tax is paid when the gain is realized, i.e., when the
bond matures.
4. Calculate the present value of the following stream of payments:
$2100 in 2 years
$2100 in 4 years
$2100 in 6 years
.
.
.
.
.
.
$2100 continuing in this pattern forever
.
The annual rate of interest is 10 percent.
1
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5. You need $129,200 at the end of seventeen years. You know that the best you can do
is to make equal payments into an account on which you can earn 9 percent interest
compounded annually. Your first payment is to be made at the end of the first year
and the final payment is to be made at the end of the 17th year.
(a) What amount must you plan to pay annually to achieve your objective?
(b) Instead of making annual payments, you decide to make one lumpsum payment
today. To achieve your objective of $129,200 at the end of the seventeen year pe
riod, what should this sum be? (You can still earn 9 percent interest compounded
annually on your account.)
6. At a growth rate of x percent, how long does it take a sum to double?
7. A woman wants to invest enough on her 40th birthday to provide her with a $5,000
annual pension that begins (the first payment is received) on her 60th birthday and
ends (the last payment is received) on her 74th birthday. If the interest rate is 6 percent
a year, what must she invest on her 40th birthday to assure herself of this pension?
8. A firm is attempting to arrange a loan from a bank to purchase some equipment. The
firm has talked to four different banks and received loan terms from each. Calculate
the rate of return the firm would be paying in each case:
(a) Bank A loans $10,000 today to the firm; the firm pays the bank $15,385 at the
end of five years.
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 Summer '06
 TimothyDreyer
 Finance, Interest Rates, Time Value Of Money, Interest, Interest Rate, Zerocoupon bond, pure discount bond

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