An annuity pays $50 per year for 20 years. What is the future value (FV) of this annuity at the end of those 20 years, given that the discount rate is 7%?

Question

BlackTom AI · Accepted Answer

We’re evaluating the future value of an ordinary annuity with constant payments.
Option A: 50 per year for 20 years, interest 7% per year. The FV formula for an ordinary annuity is FV = PMT × [((1 + i)^n − 1) / i]. Substituting PMT = 50, i = 0.07, n = 20 gives FV ≈ 50 × [((1.07)^20 − 1) / 0.07].
First compute (1.07)^20 ≈ 3.8697. Then subtract 1 to get ≈ 2.8697. Divide by 0.07 to obtain ≈ 40.9957. Multiply by 50 to get ≈ 2049.785, which rounds to about 2,049.79. This closely matches 2,049.77 depending on rounding steps. Therefore, option A is the correct FV value.
Option B: 684.76 is far smaller and would result if either the payment were much lower, the rate much higher, or the time horizon much shorter; it does not align with the standard FV formula for these inputs.
Option C: 326.44 is also far below the computed FV and would require an extremely small accumulation factor, inconsistent with 20 years at 7% with $50 payments.
Option D: 1,524.24 is closer to a partial accumulation or misapplied period convention (e.g., treating payments as due at the beginning of periods or using a different formula), but it still does not match the correct FV expression for an ordinary annuity with these parameters.
In summary, the calculation using FV = PMT × [((1 + i)^n − 1) / i] yields about 2,049.78, making option A the correct choice. The other options result from incorrect application of the formula or wrong assumptions about timing or rate effects.

An annuity pays $50 per year for 20 years. What is the future value (FV) of this annuity at the end of those 20 years, given that the discount rate is 7%?单项选择题

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