what is the compound interest on a three - year, $100.00 loan at a 10 percent annual interest…

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula is $A = P(1 + r)^n$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $n$ is the number of years. Here, $P=$100$, $r = 0.1$ (since $10%=0.1$), and $n = 3$.

Step2: Calculate the amount $A$

$A=100\times(1 + 0.1)^3=100\times(1.1)^3=100\times1.331=$133.1$.

Step3: Calculate the compound interest

Compound interest $CI=A - P$. Substitute $A = 133.1$ and $P = 100$ into the formula. $CI=133.1-100=$33.1$.

Answer:

$33.10$ (corresponding to the third option)