Compound Interest Practice Problems
1)
a.
b.
c.
Find the future value of an investment with the following properties:
Principal = $5000, Annual rate = 5.5%, Time = 3 years, Compounding = quarterly
Ans: $5890.34
Principal = $4250, Annual rate = 2.35%, Time = 10 years, Compounding = monthly
Ans: $5374.63
Principal = $17500, Annual rate = 3.6%, Time = 5 years, Compounding = daily
Ans: $20951.12
2)
Find the yield for each part of the previous problem, rounding to three decimal places. You will
have to change the assumption that the time period is for 1 year to be able to use the formula
given in class and in the text.
Answer: (a) 5.614% (b) 2.375% (c) 3.665%
3)
Find the annual percentage rate if you are given the following information, rounding to three
decimal places.
Yield = 3.785%, Compounding = yearly, Principal = $5000
Ans. 3.785%
Yield = 4.522%, Compounding = daily, Principal = $1,000,000
Ans. 4.423%
Yield = 10.25%, Compounding = weekly, Principal = $5000
Ans. 9.767%
Explain why the yield and the annual percentage rate are the same in part (a).
a.
b.
c.
d.
4)
a.
b.
c.
Find the future value of an investment with the following properties:
Principal = $5000, Annual rate = 5.5%, Time = 3 years, Compounding = continuously
Ans: $5896.97
Principal = $4250, Annual rate = 2.35%, Time = 10 years, Compounding = continuously
Ans: $5375.86
Principal = $17500, Annual rate = 3.6%, Time = 5 years, Compounding = continuously
Ans: $20951.30
5)
Find the yield for part of the previous problem, rounding to three decimal places. You will
have to change the assumption that the time period is for 1 year to be able to use the formula
given in class and in the text.
Answer: (a) 5.654% (b) 2.378% (c) 3.666%
6)
Find the annual percentage rate if you are given the following information, rounding to three
decimal places.
Yield = 3.785%, Compounding = continuously, Principal = $5000
Ans. 3.715%
Yield = 4.522%, Compounding = continuously, Principal = $1,000,000
Ans. 4.4233%
Yield = 10.25%, Compounding = continuously, Principal = $5000
Ans. 9.758%
a.
b.
c.
7)
a.
b.
c.
Find the Present Value of an amount of money that is worth the amount specified in the future:
Future value = $6000, Compounding = annually, Annual rate = 6.2%, Time = 5 years
Ans. $4441.49
Future value = $10000, Compounding = monthly, Annual rate = 7.5%, Time = 10 years
Ans. $4734.70
Future value = $12000, Compounding = annually, Yield = 5.5%, Time = 7 years
Ans. $8249.24
8)
When Lindsay Gonzalez was born, her grandfather made an initial deposit of $3000 in an
account for her college education. Assuming an interest rate of 6% compounded quarterly, how
much will be in the account in 18 years?
Ans: $8763.47
9)
Linda Davis borrowed $25900 from her father to start a flower shop. She repaid him after 11
months with simple annual interest (i.e. you compound once a year) of 8.4%. Find the total
amount she repaid.
Ans: $27877.52
10) Tanya’s Nail and FishNChips Shop has agreed to pay $2.9 million in 5 years to settle a lawsuit
due to an unfortunate accident in her place of business. (Thanks to Team 3 for the inspiration
for this problem.) How much must she invest now in an account paying 8% compounded
monthly to ha ve that amount when it is due?
Ans: About 1.9465 million dollars…she may have to declare bankruptcy unless she sells a lot
of fish and paint a lot of nails.
11) Two partners agree to invest equal amounts in their business. One will contribute $10,000
immediately. The other plans to contribute an equivalent amount in 3 years, when she expects
to acquire a large amount of money. How much should she contribute at that time to match her
partner’s investment now, assuming each grows at an annual interest rate of 6% compounded
semi-annually (twice a year)?
Ans: $11,940.52
12) Try Exercise 16 from the Compound Interest section of Project2.ppt.
13) Repeat Example 8 from the Compound Interest section of Project2.ppt but change it to a
situation where the computer costs $1899, the loans is repaid after 36 months, and the interest
rate is 5.9%. Calculate the total interest paid under these conditions. Show your calculations.
Ans: $57.69. Total interest paid is $177.67.
14) Excel has an easy way to compute the payment on a loan. Use the Insert Functions command to
invoke the PPT command. Experiment with the tool given there until you can get the same
answers (or ones that are within a few pennies) as what you get in #11 and #12. Exp lain the one
thing you need to be careful with when using the PMT command.