an employee puts $5,000 into a retirement account that offers 9.5 interest compounded annually. the employee…

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$.