What is the future value of $500 invested at 8% annual interest for 3 years, compounded annually?

What is the future value of $500 invested at 8% annual interest for 3 years, compounded annually?

• A. 580.00
• B. 600.00
• C. 629.86
• D. 700.00

Answer: (C)

With annual compounding, each year the investment grows by a factor of 1 plus the interest rate. So for three years the growth factor is 1.08^3. Compute 1.08^3 = 1.259712. Multiply by the initial amount: 500 × 1.259712 = 629.856. Rounding to the nearest cent gives 629.86. You can see it step by step as well: after year one you have 500 × 1.08 = 540; after year two: 540 × 1.08 = 583.20; after year three: 583.20 × 1.08 = 629.856, which matches the final amount. The other numbers don’t reflect three years of growth at 8% with compounding, so they’re not the correct future value.

With annual compounding, each year the investment grows by a factor of 1 plus the interest rate. So for three years the growth factor is 1.08^3.

Compute 1.08^3 = 1.259712. Multiply by the initial amount: 500 × 1.259712 = 629.856. Rounding to the nearest cent gives 629.86.

You can see it step by step as well: after year one you have 500 × 1.08 = 540; after year two: 540 × 1.08 = 583.20; after year three: 583.20 × 1.08 = 629.856, which matches the final amount.

The other numbers don’t reflect three years of growth at 8% with compounding, so they’re not the correct future value.