What is the future value (FV) of an ordinary annuity where \$500 is invested at the end of each year for 20 years at an annual interest rate of 10%? (Use the formula: \(FV = PMT \times \frac{(1 + r)^n - 1}{r}\), where \(PMT = 500\), \(r = 0.10\), \(n = 20\).)

• A. \$28,645.50
• B. \$25,000.00
• C. \$31,526.25
• D. \$20,000.00

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the formula for the future value (FV) of an ordinary annuity. The formula is: FV = PMT × ((1 + r)^n - 1) / r, where PMT is the payment amount, r is the annual interest rate, and n is the number of periods.
2. Step 2: Identify the given values from the problem. Here, PMT = 500 (payment made at the end of each year), r = 0.10 (annual interest rate), and n = 20 (number of years).
3. Step 3: Substitute the given values into the formula. Replace PMT with 500, r with 0.10, and n with 20 in the formula: FV = 500 × ((1 + 0.10)^20 - 1) / 0.10.
4. Step 4: Break down the calculation into smaller parts. First, calculate (1 + r)^n, which is (1 + 0.10)^20. Then subtract 1 from the result to find ((1 + r)^n - 1). Finally, divide this value by r (0.10).
5. Step 5: Multiply the result from Step 4 by PMT (500) to find the future value (FV). This will give you the total amount accumulated after 20 years of investing \$500 annually at a 10% interest rate.