Question

an employee puts $5,000 into a retirement account that offers 9.5 interest compounded annually. the employee makes no additional deposits or withdrawals. what is the amount of interest the employee will have earned at the end of 5 years?

Explanation:

Step1: Identify the compound interest formula

The formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$, where:

• $A$ is the amount of money accumulated after $n$ years, including interest.
• $P$ is the principal amount (the initial amount of money).
• $r$ is the annual interest rate (decimal).
• $n$ is the number of times that interest is compounded per year.
• $t$ is the time the money is invested for in years.

Here, the interest rate is given as 9.5% (assuming "9:5" is a typo and should be 9.5%), so $r = 0.095$, $P = 5000$, $n = 1$ (compounded annually), and $t = 5$.

Step2: Calculate the amount $A$

Substitute the values into the formula:
$A = 5000(1 + \frac{0.095}{1})^{1\times5}$
$A = 5000(1.095)^{5}$

First, calculate $(1.095)^{5}$. Using a calculator, $(1.095)^{5} \approx 1.095\times1.095\times1.095\times1.095\times1.095 \approx 1.57423$.

Then, $A = 5000\times1.57423 \approx 7871.15$.

Step3: Calculate the interest earned

The interest earned $I$ is $A - P$.
$I = 7871.15 - 5000 = 2871.15$.

Answer:

The amount of interest earned is approximately $\$2871.15$.