What is the future value of \$1,000 invested for 15 years at an annual interest rate of 5%, compounded annually?

• A. \$2,078.93
• B. \$2,079.00
• C. \$1,500.00
• D. \$1,750.00

Answer: (A)

Verified step by step guidance

1. Identify the formula for future value with annual compounding: \( FV = PV \times (1 + r)^n \), where \( FV \) is the future value, \( PV \) is the present value, \( r \) is the annual interest rate, and \( n \) is the number of years.
2. Substitute the given values into the formula: \( PV = 1000 \), \( r = 0.05 \) (5% as a decimal), and \( n = 15 \). The formula becomes \( FV = 1000 \times (1 + 0.05)^{15} \).
3. Simplify the expression inside the parentheses: \( 1 + 0.05 = 1.05 \). The formula now becomes \( FV = 1000 \times (1.05)^{15} \).
4. Calculate the exponent \( (1.05)^{15} \) to determine the growth factor over 15 years.
5. Multiply the result of \( (1.05)^{15} \) by \( 1000 \) to find the future value of the investment.