Answer:
We need to use the future value of an investment formula:
[tex]F = PV (1 + i)^{n}[/tex]
Where:
a. Four years at an interest rate of 7% per year.
[tex]F = 1,000 (1 + 0.07)^{4} \\F = 1,310[/tex]
b. Eight years at an interest rate of 7% per year.
[tex]F = 1,000 (1 + 0.07)^{8\\\\[/tex]
[tex]F = 1,718[/tex]
c. Four years at an interest rate of 14% per year.
[tex]F = 1,000 (1 + 0.14)^{4} \\F = 1,688[/tex]
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.