Question

what is the compound interest on a three-year, $100.00 loan at a 10 percent annual interest rate?
$10.00
$21.00
$33.10
$46.41

Explanation:

Step1: Recall compound interest formula

The compound interest formula is $A = P(1 + r)^n$, 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 $n$ is the number of years. The compound interest $CI$ is $A - P$.

First, convert the interest rate to decimal: $r = 10\% = 0.1$. $P = \$100$, $n = 3$.

Step2: Calculate the amount $A$

Substitute the values into the formula: $A = 100(1 + 0.1)^3$.

Calculate $(1 + 0.1)^3 = 1.1^3 = 1.331$.

Then $A = 100\times1.331 = 133.1$.

Step3: Calculate compound interest $CI$

$CI = A - P = 133.1 - 100 = 33.1$. So the compound interest is $\$33.10$.

Answer:

C. $33.10$