MATH 400 (Theory of Interest) Exam #1
Review Questions
The actual exam will consist of the questions here except that the portions in
red will be different.
1. A person invests $1000 at 8% simple interest for 20
years. Find the effective rate of interest for year 20.
2. If an investment of $5000 earns 8% simple interest per
year for 10 years, find the equivalent nominal rate of
interest compounded monthly.
3. If an investment of $5000 earns 6% simple interest per
year beginning today, find the point in time where the
accumulated amount will earn the equivalent to an effective
rate of 3% exactly one year later.
4. Find the annual rate of interest equivalent to an annual
rate of discount of 7.5%.
5. A person plans to invest $5000 at 8% simple interest
for the months of January and February 2010. Find the
amount of interest received, if the interest is computed
using
(a) exact simple interest (the actual/actual method).
(b) ordinary simple interest (the 30/360 method).
(c) the Banker’s Rule.
6. Find the number of years required for $500 invested at
8% interest compounded quarterly to grow to $800.
7. Find the amount that must be invested at a compound
discount of 5% compounded monthly in order to
accumulate to $5000 at the end of 10 years.
8. If $4000 invested at discount compounded monthly
grows to $6125 in 6 years, find the annual rate of discount.
9. Assuming interest of 6.2% compounded continuously,
what is the present value of $1,000,000 payable in 30 years.
10. Find the effective annual rate of 6.4% interest
compounded daily (i.e., 365 times a year).
11. Find the amount of that must be invested at 4%
interest converted quarterly in order to accumulate to the
same amount in 5 years as $400 invested at 6% discount
converted annually.
12. Find the number of years required for $500 invested at
12% interest compounded continuously to have the same
value as $1000 invested at 6% interest compounded
annually.
13. The effective rate of interest for one investment is
in = 0.n12 . If the accumulated amount at the end of year 2
was $9497.60, what was the original amount invested.
14. If t =
t
,
t 4
2
find the amount to which $800 will
accumulate in 4 years.
15. In order to receive $1000 at the end of 3 years, a
person pays $200 now and a final payment at the end of 6
years. Assuming 8% interest compounded annually, find
the amount of the final payment.
16. If a(t) = 2  02.05t for t < 40, find each of the following:
(a) the effective annual interest rate for year 10.
(b) the force of interest at the end of year 10.
17. Assuming 7% interest converted annually, find the
time at which a payment of $3000 at the end of 5 years and
a payment of $12,000 at the end of 10 years is equivalent to
one payment of $15,000 by using each of the following
methods:
(a) the method of equated time.
(b) solving for the time exactly.
18. Find the nominal rate of interest compounded
quarterly so that a payment of $3000 now is equivalent to a
payment of $1500 in 3 years and a payment of $2000 in 6
years.
19. Find the amount to which $1000 will accumulate if it
is invested at 8% interest compounded semi-annually for
4.37 years, assuming simple interest for the final fractional
period.
20. Fund A grows at 6% compounded semi-annually, and
fund B grows at 8% compounded quarterly. At the end of
5 years, fund A is $500 larger than fund B, but at the end of
10 years the funds are equal in value. Find the original
investment in fund B.
Answers to MATH 400 (Theory of Interest) Exam #1
Review Questions
1.
i20 = 0.031746
2.
i(12) = 0.0589
3.
t = 17.667 years
4.