If you receive $161 each month for 12 months and the discount rate is 0.04, what is the future value?

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BlackTom AI · Accepted Answer

Question restatement: You receive 161 dollars each month for 12 months, and the discount rate is 0.04. What is the future value?

Step-by-step analysis of how to approach this:
- First, identify the type of cash flow: a level monthly payment of 161 for 12 periods constitutes an ordinary annuity (payments at the end of each month) unless otherwise specified.
- Determine the per-period rate: if the annual discount rate is 0.04, the monthly rate i is 0.04 / 12 = 0.0033333333 (approximately 0.3333%). This is the conventional way to convert an annual rate to a monthly rate for monthly cash flows.
- Use the future value of an ordinary annuity formula for monthly periods: FV = PMT × [((1 + i)^n − 1) / i], where PMT = 161, i = 0.0033333, n = 12.
- Compute (1 + i)^n: (1.0033333)^12 ≈ 1.040741, so (1 + i)^n − 1 ≈ 0.040741.
- Divide by i: 0.040741 / 0.0033333 ≈ 12.2223.
- Multiply by the payment: 161 × 12.2223 ≈ 1967.8.
- Therefore, the standard calculation yields a future value around 1,967.8 dollars.

Now, consider potential reasons the given answer might differ:
- If you treated the payments as an annuity due (payments at the beginning of each month), you would multiply the ordinary annuity value by (1 + i) to account for one extra month of interest for each payment. That would give approximately 1967.8 × 1.0033333 ≈ 1974.0 dollars, which is still below 1996.71.
- If the monthly rate was computed differently (for example, using an effective monthly rate derived from a different interpretation of the 0.04 rate), the result could shift, but the standard interpretation of 0.04 annual discount rate yields around 1,968.
- Rounding differences in intermediate steps or calculator precision can cause small deviations, but a jump from ~1,968 to 1,996.71 is relatively large for typical rounding errors.

Evaluating the provided answer of 1996.71:
- With the standard assumptions (monthly rate = 0.04/12, ordinary annuity), the computed FV is about 1,967.8, not 1,996.71.
- The discrepancy suggests either a different interpretation of timing (e.g., payments occurring at irregular intervals), a different rate conversion (e.g., using a different monthly rate), or an arithmetic mismatch.

Summary: Using the conventional approach for monthly payments (an ordinary annuity with i = 0.04/12), the future value is approximately 1,967.8 dollars. The provided answer 1,996.71 does not align with this standard calculation under common assumptions, and the discrepancy would need clarification on timing (end vs. beginning of period) or rate definition to reconcile.

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If you receive $161 each month for 12 months and the discount rate is 0.04, what is the future value?

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