If you invest \$10 today in an account that earns an annual interest rate of 5\% compounded annually, how much will you have at the end of 3 years?

• A. \$11.58
• B. \$11.50
• C. \$12.00
• D. \$15.00

Answer: (A)

Verified step by step guidance

1. Understand the concept of compound interest: Compound interest is calculated on the initial principal and also on the accumulated interest from previous periods. The formula for compound interest is: \( A = P \times (1 + r)^n \), where \( A \) is the future value, \( P \) is the principal amount, \( r \) is the annual interest rate, and \( n \) is the number of years.
2. Identify the given values from the problem: \( P = 10 \) (initial investment), \( r = 0.05 \) (annual interest rate expressed as a decimal), and \( n = 3 \) (number of years).
3. Substitute the given values into the compound interest formula: \( A = 10 \times (1 + 0.05)^3 \).
4. Simplify the expression inside the parentheses: \( 1 + 0.05 = 1.05 \), so the formula becomes \( A = 10 \times (1.05)^3 \).
5. Calculate \( (1.05)^3 \) and then multiply the result by \( 10 \) to find the future value \( A \). This will give you the amount in the account at the end of 3 years.