What is the present value of an ordinary annuity of PMT = 100 for n = 3 at i = 5%?

What is the present value of an ordinary annuity of PMT = 100 for n = 3 at i = 5%?

• A. 272.32
• B. 300.00
• C. 283.33
• D. 285.00

Answer: (A)

Understanding how to value a series of equal payments made at the end of each period is key. This is the present value of an ordinary annuity: each payment is discounted back to today and then summed. PV of an ordinary annuity equals PMT times the factor [1 − (1 + i)^(-n)] / i. With PMT = 100, i = 0.05, n = 3, that factor is [1 − (1.05)^(-3)] / 0.05 = 2.723248. Multiply by 100 to get the present value: 272.3248, which rounds to 272.32. Equivalently, sum the discounted payments: 100/1.05 + 100/1.05^2 + 100/1.05^3 ≈ 95.2381 + 90.7029 + 86.3838 ≈ 272.3248. Note: if the payments were at the beginning of each period (an annuity due), the value would be higher by a factor of (1 + i).

Understanding how to value a series of equal payments made at the end of each period is key. This is the present value of an ordinary annuity: each payment is discounted back to today and then summed.

PV of an ordinary annuity equals PMT times the factor [1 − (1 + i)^(-n)] / i. With PMT = 100, i = 0.05, n = 3, that factor is [1 − (1.05)^(-3)] / 0.05 = 2.723248. Multiply by 100 to get the present value: 272.3248, which rounds to 272.32.

Equivalently, sum the discounted payments: 100/1.05 + 100/1.05^2 + 100/1.05^3 ≈ 95.2381 + 90.7029 + 86.3838 ≈ 272.3248.

Note: if the payments were at the beginning of each period (an annuity due), the value would be higher by a factor of (1 + i).