These are the solutions to the savings plan exercises. You are strongly advised to work out your own solutions before you look at these.
1. A woman invests $50 a month for 40 years into an account earning 4.8% compounded monthly.
A. How much is in the account after 40 years?
Based on the formula, the future value is $72,436.07. Based on the table illustrating the growth of the account balance, the future value is $72,436.21. Remember that the table takes into account the rounding of the periodic interest to the nearest penny and the formula does not.
B. How much interest will have been earned?
Based on the formula, the total interest earned is $48,436.07. When the periodic interest values are rounded to the nearest penny, the total interest earned is $48,436.21.
C. What is the annual percentage yield?
The annual percentage yield is 4.907%.
Calculator Solution for A, B and C
D. Table (partial) showing the growth of the account balance:
E. Line graph illustrating the growth of the account balance:
2. A woman wants to save up $18,000 to buy a new car in five years. She invests regularly into a savings account earning 5.4% compounded monthly.
A. What is the size of her monthly investment?
She should invest $261.99 a month.
B. How much interest will she earn?
Based on the formula, the total interest earned will be $2,280.60. However, the actual total interest will be $2,280.50. (Notice that she will actually come up ten cents short of her stated goal.)
C. What is the annual percentage yield?
The annual percentage yield is 5.536%.
Calculator Solution for A, B and C
D. Table (partial) showing the growth of the account balance:
E. Line graph illustrating the growth of the account balance:
3. A couple invests $1,000 every six months for 30 years into a retirement account earning 4.7% compounded semiannually.
A. What is the future value of this investment?
Based on the formula, the future value is $128,922.66. Based on the table illustrating the growth of the account balance, the future value is $128,922.63. Remember that the table takes into account the rounding of the periodic interest to the nearest penny and the formula does not.
B. How much total interest will they earn?
Based on the formula, the total interest earned is $68,922.66. When the periodic interest values are rounded to the nearest penny, the total interest earned is $68,922.63.
C. What is the annual percentage yield?
The annual percentage yield is 4.755%.
Calculator Solution for A, B and C
D. Table (partial) showing the growth of the account balance:
E. Line graph illustrating the growth of the account balance:
4. A couple wants to save $500,000 for their retirement in 20 years. They make monthly payments into an account paying 6.6% compounded monthly.
A. What is the size of their monthly investment?
They should invest $1,007.36 a month.
B. How much interest will they earn?
Based on the formula, the total interest earned will be $258,233.60. However, the actual total interest will be $258,233.46. (Notice that they will actually come up 14 cents short of their stated goal.)
C. What is the annual percentage yield?
The annual percentage yield is 6.803%.
Calculator Solution for A, B and C
D. Table (partial) showing the growth of the account balance:
E. Line graph illustrating the growth of the account balance:
