What is the compound interest on a three-year, $100.00 loan at a 10 percent annual interest rate?

What is the compound interest on a three-year, $100.00 loan at a 10 percent annual interest rate?

a. $10.00

b. $21.00

c. $33.10

d. $46.41

Answer: c. $33.10

To compute the total interest compounded on it for three years, we have $100.00 loan at a 10% annual interest rate, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

A = Final amount (principal + interest)

P = Initial principal amount

r = Annual interest rate (in decimal form)

n = Number of times the interest is compounded per year (for annual compounding, n = 1)

t = time in years

Given:

P = $100.00

r = 0.10 (10% expressed in decimal form)

n = 1 (for annual compounding)

t = 3 years

Substituting the values in the formula:

A = 100(1 + 0.10/1)^(1 * 3)

A = 100(1.10)^3

A = 100 *(1.331)

A = $133.10

Since the initial principal amount was $100, the compound interest earned over three years is:

Compound Interest = A – P

Compound Interest = $133.10 – $100.00

Compound Interest = $33.10

Thus, the interest on the same amounts for three years, under the compound interest rate is $33.10.