To solve this problem we will use the formula for compound interest:
[tex]P_N=P_0\cdot(1+\frac{r}{k})^{N\cdot k}\text{.}[/tex]Where:
• P_N is the balance in the account after N years,
,• P_0 is the starting balance of the account (also called an initial deposit, or principal),
,• r is the annual interest rate in decimal form,
,• k is the number of compounding periods in one year.
In this problem, we have:
• P_0 = $4200,
,• r = 8.75% = 0.0875,
,• k = 1 (the interest is compounded anually),
,• N = 14 years.
Replacing these data in the formula above, we get:
[tex]P_{14}=\text{ \$4200 }\cdot(1+\frac{0.0875}{1})^{14\cdot1}=\text{ \$13591}.24.[/tex]Answer
The investment would be worth $13591.24 after 14 years.
