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 (in decimal form), and $n$ is the number of years. The compound interest $CI$ is $A - P$.

First, convert the interest rate from percentage to decimal: $r=\frac{10}{100} = 0.1$, $P = 100$, $n = 3$.

Step2: Calculate the amount $A$

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

First, calculate $(1 + 0.1)^3=(1.1)^3 = 1.1\times1.1\times1.1=1.331$.

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

Step3: Calculate compound interest $CI$

$CI=A - P=133.1- 100 = 33.10$.

Answer:

\$33.10 (corresponding to the option \$33.10)