If you receive $178 each month for 12 months and the discount rate is 0.05, what is the future value?

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BlackTom AI · Accepted Answer

The problem asks for the future value of a series of monthly payments of 178 dollars over 12 months when the discount/interest rate is 0.05. To compute the future value of an ordinary annuity with monthly contributions, we use the formula FV = P * [((1 + i)^n - 1) / i], where P is the payment per period, i is the per-period interest rate, and n is the number of periods.

Step 1: Determine the per-period rate. If 0.05 is an annual rate and we assume monthly compounding, the monthly rate i = 0.05 / 12 ≈ 0.0041667.

Step 2: Identify the number of periods. There are n = 12 monthly payments.

Step 3: Compute the accumulation factor: (1 + i)^n = (1.0041667)^12. This value is approximately 1.05116.

Step 4: Subtract 1: (1 + i)^n - 1 ≈ 0.05116.

Step 5: Divide by i: 0.05116 / 0.0041667 ≈ 12.278, which is the factor by which each 178 payment is accumulated to the end of month 12.

Step 6: Multiply by the payment: 178 * 12.278 ≈ 2188.0.

Putting the pieces together, the computed future value under this standard interpretation is approximately 2188.0. If a different interpretation of the rate or compounding is intended (for example, treating 0.05 as a per-period rate or using a different timing convention for payments), the result will differ, and you would adjust i and possibly n accordingly. In such alternate scenarios, one would substitute the new i and possibly a different n into the same FV formula to obtain the corresponding future value.

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If you receive $178 each month for 12 months and the discount rate is 0.05, what is the future value?

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