Question

A principal of $4200 is invested at 8.75% Interest, compounded annually. How much will the investment be worth after 14 years?

Answer 1

To solve this problem we will use the formula for compound interest:

$P_N=P_0\cdot(1+\frac{r}{k})^{N\cdot k}\text{.}$

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:

$P_{14}=\text{ \ 4200 }\cdot(1+\frac{0.0875}{1})^{14\cdot1}=\text{ \ 13591}.24.$

Answer

The investment would be worth $13591.24 after 14 years.