Question

derek deposited $7,615 in an account earning 10% interest compounded annually. to the nearest cent, how much interest will he earn in 2 years?

Explanation:

Step1: Recall compound interest formula

The compound interest formula is $A = P(1 + r)^t$, 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), and $t$ is the time the money is invested for in years. First, we need to find the amount $A$ after 2 years, then subtract the principal $P$ to get the interest earned.

Step2: Convert the interest rate to decimal

The annual interest rate $r$ is 10%, which as a decimal is $r = 0.10$.

Step3: Identify the principal and time

The principal $P = \$7615$ and the time $t = 2$ years.

Step4: Calculate the amount $A$

Using the compound interest formula $A = P(1 + r)^t$, substitute the values:
$A = 7615(1 + 0.10)^2$
First, calculate $(1 + 0.10)^2 = 1.10^2 = 1.21$.
Then, $A = 7615\times1.21$.
Calculate $7615\times1.21$:
$7615\times1.21 = 7615\times(1 + 0.2 + 0.01) = 7615\times1 + 7615\times0.2 + 7615\times0.01 = 7615 + 1523 + 76.15 = 9214.15$.

Step5: Calculate the interest earned

The interest earned $I$ is $A - P$.
So, $I = 9214.15 - 7615 = 1599.15$.

Answer:

$\$1599.15$