What is the future value of an ordinary annuity paying 200 per year for 7 years at 8%?

What is the future value of an ordinary annuity paying 200 per year for 7 years at 8%?

• A. 1700.00
• B. 1784.56
• C. 1800.00
• D. 1900.00

Answer: (B)

The future value of an ordinary annuity captures how each end-of-period payment grows with interest until the end of the term. For this, the formula is FV = PMT × [((1 + i)^n − 1) / i], since every payment earns interest for the remaining periods and the last payment is included at its face value. Here, the payment is 200, the interest rate is 8% (0.08), and there are 7 years. Compute (1.08)^7 ≈ 1.713824, subtract 1 to get 0.713824, divide by 0.08 to get ≈ 8.922806, and multiply by 200 to obtain ≈ 1784.56. So the future value is about 1,784.56. If the payments were at the beginning of each year (an annuity due), the value would be larger because each payment would accumulate for one more year.

The future value of an ordinary annuity captures how each end-of-period payment grows with interest until the end of the term. For this, the formula is FV = PMT × [((1 + i)^n − 1) / i], since every payment earns interest for the remaining periods and the last payment is included at its face value.

Here, the payment is 200, the interest rate is 8% (0.08), and there are 7 years. Compute (1.08)^7 ≈ 1.713824, subtract 1 to get 0.713824, divide by 0.08 to get ≈ 8.922806, and multiply by 200 to obtain ≈ 1784.56.

So the future value is about 1,784.56. If the payments were at the beginning of each year (an annuity due), the value would be larger because each payment would accumulate for one more year.