What is the future value of an ordinary annuity where \$400 is invested at the end of each year for 15 years at an annual interest rate of 6%?

• A. \$9,635.20
• B. \$8,400.00
• C. \$10,200.00
• D. \$9,457.60

Answer: (A)

Verified step by step guidance

1. Step 1: Understand the problem. The future value of an ordinary annuity is calculated when equal payments are made at the end of each period, and interest is compounded annually. Here, the payment (PMT) is \$400, the number of periods (n) is 15 years, and the annual interest rate (r) is 6%.
2. Step 2: Use the formula for the future value of an ordinary annuity: FV = PMT × ((1 + r)^n - 1) / r. This formula accounts for the compounding effect of interest over time.
3. Step 3: Substitute the given values into the formula. Replace PMT with 400, r with 0.06 (6% expressed as a decimal), and n with 15. The formula becomes: FV = 400 × ((1 + 0.06)^15 - 1) / 0.06.
4. Step 4: Calculate the term (1 + r)^n. This involves raising (1 + 0.06) to the power of 15. Then subtract 1 from the result to find the numerator of the formula.
5. Step 5: Divide the numerator by the interest rate (0.06) to complete the calculation. Multiply the result by the payment amount (\$400) to find the future value of the annuity.