Question

An employee puts $5,000 in a retirement account that offers 9% interest compound annually. The employee makes no additional deposits or withdrawals. Which amount is closest to the interest the employee will have earned at the end of 5 years?

Answer 1

I = 2693.14

Explanation:

To find the interest earned at the end of 5 years, we can use the compound interest formula:

where:

- $A$ is the future value of the investment

- $P$ is the principal amount

- $r$ is the annual interest rate as a decimal

- $n$ is the number of times interest is compounded per year

- $t$ is the time in years

Plugging in the given values, we get:

$$A = 5000 (1 + 0.09/1)^{1 \times 5}$$

$$A = 5000 (1.09)^5$$

$$A = 7693.14$$

The interest earned is the difference between the future value and the principal amount:

$$I = A - P$$

$$I = 7693.14 - 5000

I = 2693.14

Therefore, the interest earned at the end of 5 years is **$2693.14**.