What is the interest earned after 2 years on a $1000 loan at 5% annual compound interest?

What is the interest earned after 2 years on a $1000 loan at 5% annual compound interest?

• A. $50
• B. $102.50
• C. $105
• D. $150

Answer: (B)

When interest compounds, each year's interest is earned on the previous balance. The amount after two years is 1000 × (1 + 0.05)^2. Since (1.05)^2 = 1.1025, the balance becomes 1000 × 1.1025 = 1102.50. The interest earned is 1102.50 − 1000 = 102.50. So the interest earned after 2 years is 102.50. This is higher than simple interest, which would be 100, because you’re earning interest on the interest from the first year.

When interest compounds, each year's interest is earned on the previous balance. The amount after two years is 1000 × (1 + 0.05)^2. Since (1.05)^2 = 1.1025, the balance becomes 1000 × 1.1025 = 1102.50. The interest earned is 1102.50 − 1000 = 102.50. So the interest earned after 2 years is 102.50. This is higher than simple interest, which would be 100, because you’re earning interest on the interest from the first year.