Math 166 Week-in-Review - © S. Nite 10/26/2012
WIR #7
Page 1 of 3
Week in Review #7 (F.1-F.4)
Simple Interest
I = Prt, where I is the interest, P is the principal, r is the interest rate, and t is the time in years.
A = P(1 + rt), where A is the accumulated amount, P is the principal, r is the interest rate, and t is
the time in years.
Present Value and Future Value of Loans, Annuities, and Sinking Funds
Use TVM solver, enter known information and press ALPHA – Enter with cursor on PV (or FV)
to solve for present value (or future value). Note: PMT = 0 if there is a one-time deposit/loan; PV
or FV = 0 if there are regular payments with nothing in the beginning.
Discounts
The discount, D on a discounted loan of M dollars at a sample annual interest rate of r for t years
is D = Mrt
Where D = discount (interest paid at time of loan)
M = maturity value (amount borrowed)
r = discount rate (annual simple interest rate)
t = length of loan.
The proceeds P of the loan is the actual amount the borrower receives when the loan is made
and is given by P = M – D.
Effective Rate of Interest
r
For discounted loans, the effective rate of interest is reff =
, where r is the interest rate and t
1 − rt
is the number of years..
n
For regular loans, ref
r

=  1 +  − 1 , where re is the effective rate of interest, r is the
n

annual interest rate, and n is the number of compounding periods per year.
Compound Interest
Earned interest that is periodically added to the principal and thereafter itself earns interest at the
same rate is called compound interest.
nt
 r
A = P1 +  , where A is the accumulated amount, P is the principal, r is the annual interest
 n
rate, n is the number of compounding periods per year, and t is the time in years. Use TVM
solver in the calculator.
Continuous Compounding of Interest
A = Pe rt , where A is the accumulated amount, P is the principal, r is the annual interest rate
compounded continuously, and t is the time in years.
Doubling Times Rule of 72
A good estimate for doubling time is 72 divided by the interest rate.
Math 166 Week-in-Review - © S. Nite 10/26/2012
WIR #7
Page 2 of 3
1. Mandy needs $3,200 to pay off a bill. She has taken out a discount loan that has
a monthly discount rate of 5.4%. The loan must be paid back in 8 months. How
much will Mandy pay back (i.e., what is the maturity value)?
2. Jenn has agreed to pay back a $5,300 discount loan at the end of 7 months. The
loan has an annual simple discount rate of 4.7%. What is the discount? How much
money does Jenn actually receive from the loan?
3. Find the effective yield on a discount loan with a discount rate of 6.5% for 3
months. Round your answer to two decimal places.
4. Find the simple interest on a $2,500 investment made for 4 years at an interest
rate of 5.3% per year. What is the accumulated amount?
5. A principal of $7,500 earns 4.2% per year simple interest. How long will it take
for the future value to become $8,700? Round the answer to two decimal places.
6. Find the present value of $60,000 due in 3 years at at rate of 7% per year,
compounded quarterly.
7. Find the effective yield for an account with a nominal interest rate of 10% per
year compounded semiannually, for $5,000 to grow to $8,000.
8. Find the accumulated amount if $30,000 is invested at 4.3% per year,
compounded monthly for 10 years.
9. Petro contributes $7,000 per year into a retirement account. How much will he
have after 32 years with interest earned at 6.7% per year, compounded annually?
10. The Commeros are planning to go on a cruise 3 years from now and have
agreed to set aside $150 per month for the cruise. If they deposit the money at the
end of each month into an account paying $3.5% interest per year, compounded
monthly, how much money will they have in the fund at the end of two years?
11. Dani will need $21,000 in 4 years for a new car. She is going to start with $400
and then make quarterly payments into an account with an interest rate of 4.2% per
year, compounded quarterly. What is the payment amount she needs to make?
12. Find the amount needed to deposit into an account today to yield quarterly
pension payments of $9,000 for the next 15 years if the account earns 3% per year,
compounded quarterly.
Math 166 Week-in-Review - © S. Nite 10/26/2012
WIR #7
Page 3 of 3
13. Benito and Sashi are saving for their daughter’s education at Texas A&M
University. They want to have $70,000 at the end of 15 years. How much should
they put each month into a savings account that earns an annual rate of 4%
compounded monthly? How much interest would they earn over the life of the
account? Determine the fund balance after 10 years.
14. Jin has $7000 in an account that earns 9% per year, compounded monthly.
What is the largest amount she can withdraw monthly and not affect the balance of
the account? If she withdraws $25 monthly, how much will she have at the end of
18 months?
15. A business creates a sinking fund in order to have $320,000 to replace
machinery in 15 years. How much should be deposited into the account at the end
of each quarter if the annual interest rate is 5% compounded quarterly? How much
interest would they earn over the life of the account? Determine the balance after 5
years, 10 years, and 12 years.
16. What monthly payment is required to amortize a loan of $26,000 over 6 years
at an interest rate of 8.5% per year charged on the unpaid balance and interest
calculations made at the end of each month? How much interest is paid over the
life of the loan?
17. The Juarez’s have $25,000 for a down payment on a house. They plan to spend
$1600 in monthly payments on the house. If the mortgage rate is 7.2% per year
compounded monthly for the 30-year mortgage, what price house can they afford?
18. Find the monthly payment to amortize a $220,000 mortgage loan over 30 years
at an annual interest rate of 6% compounded monthly. Find the total interest paid
on the loan.
19. Cheri is purchasing a house for $250,000. She will be making a 15% down
payment and financing the rest over 30 years at 5.2% compounded monthly. What
is the monthly payment? What will be the balance after 5 years? How much equity
will she have after 5 years?
20. A $16,000 loan is to be amortized in equal monthly payments over 5 years with
interest rate of 4% per year compounded monthly. Complete the first three rows of
an amortization table.