If you receive $158 each 6 months for 10 years and the discount rate is 0.05, what is the future value?

Question

If you receive $158 each 6 months for 10 years and the discount rate is 0.05, what is the future value?

BlackTom AI · Accepted Answer

We’re given an ordinary annuity with semiannual payments. Each payment is 158, there are 10 years of payments, so the number of periods n = 10 × 2 = 20. The discount rate is 0.05 per year, so the rate per semiannual period is i = 0.05 / 2 = 0.025. To find the future value at the end of the 10-year horizon, use the future value of an ordinary annuity formula: FV = P × [((1 + i)^n − 1) / i].

Compute (1 + i)^n: (1.025)^20 ≈ 1.6386. Subtract 1 to get 0.6386. Divide by i = 0.025 to obtain 0.6386 / 0.025 ≈ 25.543.

Multiply by the periodic payment: 25.543 × 158 ≈ 4036.5. Depending on rounding at intermediate steps, you may see 4036.06 listed as the FV. The key steps are converting the annual rate to a per-period rate, counting the total number of semiannual periods, applying the annuity FV formula, and multiplying by the payment amount.

If you had interpreted the 0.05 as a per-period rate rather than a per-year rate, you would get a different result, illustrating why it’s important to align the interest rate with the payment frequency.

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If you receive $158 each 6 months for 10 years and the discount rate is 0.05, what is the future value?

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