To solve this problem, we must use the Compound Interest formula:
[tex]P_N=P_0\cdot(1+\frac{r}{k})^{N\cdot k}.[/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 = 24,000,
,• r = 6% = 0.06%,
,• k = 1 (because the interest compounded annually),
,• N = 14.
Replacing the data in the equation above, we get:
[tex]P_{14}=24,000\cdot(1+0.06)^{14}\cong54,261.6944\cong54,262.[/tex]Answer
The amount to be paid at the end of the 14 years will be $54,262.
