Simple and Compound Interest
Sean invested $5,000.00 in mutual fund with the interest rate of 8%. How much interest will he
earn after 6 years?
2. Maria borrows $2000 for a period of eighteen months. What simple annual interest rate is being
changed if the interest that she must repay after nine months is $225?
3. You wish to borrow $8,000 for 9 months. If the person you are borrowing from offers a discounted
loan at 7%, how much must you repay at the end of the nine months?
4. An investment of $4,000 is made at an annual simple interest rate of 5%. How much additional
money must be invested at an annual simple interest rate of 9% so that the total annual interest
earned is 6% of the total investment?
5. The manager of a mutual fund placed 25% of the fund’s available cash in a 6% simple interest
account, 15% in 8% corporate bonds, and the remainder in a money market fund that earns 7%
annual simple interest. The total annual interest from the investments was $1380. What was the
total amount invested?
6. When Susan was born, her grandparents deposited $12000 into a college fund, which earned 6%
interest, compounded daily. What was the balance when Susan celebrated her 18th birthday? Use
360 days to the year.
7. Calculate the effective annual rates for 7.5% compounded continuously, and 7.6% compounded
monthly.
8. An Individual Retirement Account (IRA) has $4000 in it, and the owner decides not to add any
more money to the account other than the interest earned at 6% compounded quarterly. How
much will be in the account 30 years from the day it was opened?
9. What is the annual nominal rate (ANR) compounded monthly for a CD that has an annual
percentage yield of 4.1%?
10. How much should a $5,000 face value zero coupon bond, maturing in 15 years, be sold for now if
its rate of return is to be 6% compounded annually?
1.
Solutions
1. Sean invested $5,000.00 in mutual fund with the interest rate of 8%. How much interest will he earn after 6
years?
I = Prt
I = 5000(0.08)(6) = 2400.0
Sean earns $2,400 interest.
2. Maria borrows $2000 for a period of eighteen months. What simple annual interest rate is being changed if
the interest that she must repay after nine months is $225?
I = Prt
225 = 2000(r(0.75))
r = 0.15
Maria is paying 15%.
3. You wish to borrow $8,000 for 9 months. If the person you are borrowing from offers a discounted loan at
7%, how much must you repay at the end of the nine months?
P = A(1 − rt)
8000 = A(1 − (0.07)(0.75))
A = 8443.30
You must repay $8,443.30.
4. An investment of $4,000 is made at an annual simple interest rate of 5%. How much additional money must
be invested at an annual simple interest rate of 9% so that the total annual interest earned is 6% of the total
investment?
Let x be the additional amount of money.
P
I = rP
r
4000
x
0.05 (4000)(0.05) = 200.0
0.09
4000 + x 0.06
0.09x
0.06(4000 + x)
0.06(4000 + x) = 200 + 0.09x
x = 1333.30
The extra amount required is $1333.30.
5. The manager of a mutual fund placed 25% of the fund’s available cash in a 6% simple interest account, 15%
in 8% corporate bonds, and the remainder in a money market fund that earns 7% annual simple interest. The
total annual interest from the investments was $1380. What was the total amount invested?
Let x be the total amount invested
P
r
I = rP
0.25x 0.06 (0.06)(0.25x) = .0 15x
0.15x 0.08 (0.08)(0.15x) = .0 12x
0.6x
0.07
(0.07)(0.6x) = .0 42x
.0 15x + .0 12x + .0 42x = 1380
x = 20000
The fund manager has $20, 000 to place.
6. When Susan was born, her grandparents deposited $12000 into a college fund, which earned 6% interest,
compounded daily. What was the balance when Susan celebrated her 18th birthday? Use 360 days to the
year.
r ) mt
A = P( 1 + m
A = 12000(1 + 0.06 ) (360)(18) = 35333.0
360
Susan will have $35, 333 for her college fund.
.
7. Calculate the effective annual rates for 7.5% compounded continuously, and 7.6% compounded monthly.
r eff = e r − 1
r eff = e 0.075 − 1 = .07788 4
The effective annual rate for 7.5% compounded continuously is 7.788 4%.
r )m − 1
r eff = (1 + m
r eff = (1 + 0.076 ) 12 − 1 = .07870 4
12
The effective annual rate for 7.6% compounded monthly is 7.870 4%.
8. An Individual Retirement Account (IRA) has $4000 in it, and the owner decides not to add any more money
to the account other than the interest earned at 6% compounded quarterly. How much will be in the account 30
years from the day it was opened?
r ) mt
A = P( 1 + m
A = 4000(1 + 0.06 ) (4)(30) = 23877.0
4
There will be $23,877 in the account.
9. What is the annual nominal rate (ANR) compounded monthly for a CD that has an annual percentage yield
of 4.1%?
r )m − 1
APY = (1 + m
0.041 = (1 + r ) 12 − 1
12
r = .04024 9
The annual nominal rate is 4.0249%.
10. How much should a $5,000 face value zero coupon bond, maturing in 15 years, be sold for now if its rate
of return is to be 6% compounded annually?
A = P(1 + r) n
5000 = P(1 + 0.06) 15
P = 2086. 3
The price of the bond should be $2086.3.