These are the solutions to the compound interest exercises. You are strongly advised to work out your own solutions before you look at these.
1. A man invests $3000 for 5 years at 4.2% compounded monthly.
A. How much will be in the account at the end of the term?
The formula yields a future value of $3,699.68 but the table results in a value of $3,699.67.
B. How much interest will be earned?
The formula yields a total interest of $699.68 but the table results in $699.67 of total interest.
C. What is the annual percentage yield?
APY = 4.282% (rounded to 3 decimal places)
Calculator solution for A, B and C
D. Prepare a table that shows the growth of the investment.
E. Create a line graph illustrating the growth of the investment.
2. A woman invests $5,000 in a 18-month CD (Certificate of Deposit) paying 5.2% compounded quarterly.
A. What is the future value of the CD?
Based on the formula, the future value is $5,402.90. The table results in a future value of $5,402.91
B. How much interest will be earned?
Based on the formula, the total interest is $402.90. The table results in a total interest of $402.91.
C. What is the annual percentage yield?
APY = 5.302% (rounded to 3 decimal places)
Calculator solution for A, B and C
D. Prepare a table that shows the growth of the investment. (See below.) Notice that the actual interest and future value are one cent more than the results given by the formulas.
F. Create a line graph illustrating the growth of the investment.
3. A $500 savings bond pays 6.5% compounded semiannually and matures in 7.5 years.
A. What is the purchase price?
The purchase price is $309.47.
B. How much interest will be earned?
The total interest will be $190.53.
C. What is the annual percentage yield?
APY = 6.606% (rounded to 3 decimal places)
Calculator solution for A, B and C
D. Prepare a table that shows the growth of the investment. Notice that, once more, the table values and the formula values differ by a penny.
E. Create a line graph illustrating the growth of the investment.
4. A couple decides to invest some money in an account for use during retirement. Their goal is to have $100,000 in 40 years. The account pays 5.5% compounded monthly.
A. How much do they need to invest to meet their goal?
They will need to invest $11,136.15.
B. How much interest will they earn?
Over the 40-year term of the investment, they will earn a total of $88,863.85 in interest.
C. What is the annual percentage yield?
APY = 5.641% (rounded to 3 decimal places)
Calculator solution for A, B and C
D. Prepare a table that shows the growth of the investment.
E. Create a line graph illustrating the growth of the investment.
