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Problem Set #1
Compounding and Discounting
Page.1
Problem Set #1
Compounding and Discounting
1. Find the values of the 6month, 1year and 5year discount factors (
DF
0
.
5
,
DF
1
,
DF
5
) when
(a) the annual interest rate is 7% compounded annually;
(b) the annual interest rate is 11% compounded semiannually;
(c) the monthly interest rate is 0.8%;
(d) the continuously compounded annual interest rate is 9%;
(e) the annual interest rate is 14.6% compounded daily (assuming 365 days a year).
Show all your calculations.
2. Suppose that a savings account oﬀers you an annual interest rate of 10% compounded quar
terly. Calculate the equivalent annual rate compounded
(a) every year;
(b) semiannually;
(c) monthly;
(d) daily;
(e) continuously.
Your answers should all show 2 decimals (e.g. 9.12%). Show all your calculations.
3. You have won the Florida state lottery. Lottery oﬃcials oﬀer you the choice of the following
alternative payments:
•
Alternative 1: $10,000 one year from now.
•
Alternative 2: $20,000 ﬁve years from now.
Which alternative should you choose if the annual discount rate is
(a) 0%?
(b) 10%?
(c) 20%?
(d) What discount rate makes the two alternatives equally attractive to you?
4. Suppose you deposit $1,000 in an account at the end of each of the next four years. If the
account earns 12% annually, how much will be in the account at the end of seven years?
5. Find an expression for the exact eﬀective annual rate of interest at which payments of $300
at the present, $200 at the end of one year, and $100 at the end of two years will accumulate
to $700 at the end of two years.
6. Suppose that you invest a certain amount of money in a savings account which is earning an
annually compounded interest rate of
r
. In exactly how many years (as a function of
r
) will
that amount of money be doubled?
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View Full DocumentProblem Set #1
Compounding and Discounting
Page.2
7. Suppose that you invest $100 in a savings account which is earning an annual interest rate
of 8% (compounded annually). What is the ﬁrst year in which the interest credited to your
account for that year exceeds your original investment in the account?
8. The present value of two payments of $100 each to be made at the end of
n
years and 2
n
years is $100. Find a general expression for
n
if the annual interest rate (compounded every
year) is
r
.
9. Your parents make you the following oﬀer: they will give you $500 at the end of every month
for the next ﬁve years if you agree to pay them back $500 at the end of every month for
the following ten years. Should you accept this oﬀer if your opportunity cost is 12% a year
(compounded annually)?
10. A man aged 40 wishes to accumulate a fund for retirement by depositing $1,000 at the
beginning
of each year for 25 years. Starting at age 65, he will make 15 annual withdrawals
at the
beginning
of each year. Assuming that all payments are certain to be made, ﬁnd
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 Spring '07
 Berk

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