If you receive $144 each month for 12 months and the discount rate is 0.08, what is the future value?

Question

BlackTom AI · Accepted Answer

To find the future value of monthly payments, we treat this as an ordinary annuity where each month you receive 144 for 12 months. The discount rate given is 0.08 per year, so we convert it to a monthly rate: i = 0.08 / 12 = 0.006666... (approximately).

Next, we use the future value of an ordinary annuity formula: FV = PMT * [((1 + i)^n - 1) / i], where PMT = 144, i ≈ 0.0066667, and n = 12.

Compute the growth factor over the 12 periods: (1 + i)^n = (1.0066667)^12 ≈ 1.0830 (approximately).

Subtract 1: (1 + i)^n - 1 ≈ 0.0830. Then divide by i: 0.0830 / 0.0066667 ≈ 12.45.

Multiply by the monthly payment: FV ≈ 144 * 12.45 ≈ 1792.8.

With rounding considerations, the calculated future value is about 1,792.79. This aligns with using the standard annuity future value approach for monthly payments under a periodic rate derived from the annual rate.

If someone interpreted the rate differently (for example, using an effective annual approach without converting to monthly), the result would diverge, illustrating why converting the rate to the correct per-period basis is crucial for this calculation.

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If you receive $144 each month for 12 months and the discount rate is 0.08, what is the future value?

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