Question

Calculate the future value of $1,000 in a. Four years at an interest rate of 7% per year. b. Eight years at an interest rate of 7% per year. c. Four years at an interest rate of 14% per year. d. Why is the amount of interest earned in part (a) less than half the amount of interest earned in part (b)? b. Eight years at an interest rate of 7% per year. The future value of $1,000 in 8 years at an interest rate of 7% per year is (Round to the nearest dollar.) c. Four years at an interest rate of 14% per year. The future value of $1,000 in 4 years at an interest rate of 14% per year is (Round to the nearest dollar.) d. Why is the amount of interest earned in part (a) less than half the amount of interest earned in part (b)? (Select the best choice below.) A. This results because you earn interest on past interest. Since more interest has been paid at the end of the time period than at the beginning, the money grows faster. B. The interest earned in part (a) is based on a lower effective annual interest rate. C. The annual interest rate in part (b) is slightly higher than the rate assumed in part (a). This is because of compounding D. The amount of interest earned in part (a) is really half of the amount of interest earned in part (b) since in part (b) the money grows for twice as many years as in part (a).

Answer 1

Answer:

We need to use the future value of an investment formula:

$F = PV (1 + i)^{n}$

Where:

• F = Future value
• PV = Present value
• i = interest rate
• n = number of compounding periods

a. Four years at an interest rate of 7% per year.

$F = 1,000 (1 + 0.07)^{4} \\F = 1,310$

b. Eight years at an interest rate of 7% per year.

$F = 1,000 (1 + 0.07)^{8$

$F = 1,718$

c. Four years at an interest rate of 14% per year.

$F = 1,000 (1 + 0.14)^{4} \\F = 1,688$

d. Why is the amount of interest earned in part (a) less than half the amount of interest earned in part (b)?

The correct answer is A.

Because compound interest capitalizes. This means, that the interest earned in the first year becomes part of the principal, and from that increased principal amount, the new interest rate for the second year is calculated.