Question

nicholas has $5,495 in an account that earns 14% interest compounded annually. to the nearest cent, how much interest will he earn in 4 years?

Explanation:

Step1: Recall 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, and $t$ is the time the money is invested for in years. Since it's compounded annually, $n = 1$.
Given $P = 5495$, $r = 0.14$ (14% as a decimal), $n = 1$, $t = 4$.

Step2: Calculate the amount $A$

Substitute the values into the formula:
$A = 5495(1 + \frac{0.14}{1})^{1\times4}$
$A = 5495(1.14)^{4}$
First, calculate $1.14^{4}$: $1.14\times1.14 = 1.2996$, $1.2996\times1.14 = 1.481544$, $1.481544\times1.14 \approx 1.68896016$
Then, $A = 5495\times1.68896016 \approx 5495\times1.68896 \approx 9280.8352$

Step3: Calculate the interest earned

Interest earned $I = A - P$
$I = 9280.8352 - 5495 = 3785.8352$

Answer:

$\$3785.84$ (rounded to the nearest cent)