If the future value in one year is $7,524 and the discount rate is 0.035, what is the current price?

Question

BlackTom AI · Accepted Answer

We’re asked to find the current price (present value) given a future value of 7,524 one year from now and a discount rate of 3.5% (0.035).

First, identify the appropriate present value formula for annual discounting: PV = FV / (1 + r)^t. Here, FV = 7,524, r = 0.035, and t = 1 year, so PV = 7,524 / 1.035.

Next, perform the division to obtain the present value. Dividing 7,524 by 1.035 yields approximately 7,269.57. (A precise calculation gives PV ≈ 7,269.565..., which rounds to about 7,269.57 when using two decimal places.)

Now consider the provided answer of 7,268.12. This value is slightly lower than the computed present value. The difference could arise from rounding at an intermediate step, using a different rounding convention, or a miscalculation in the division. If one truncates instead of rounds, or if a less precise reciprocal of 1.035 is used, slight deviations like this can occur.

To verify, multiply the computed present value by (1 + r) to see if you recover the future value: 7,269.57 × 1.035 ≈ 7,524.0 (allowing for small rounding differences), which aligns with the given FV of 7,524.

In summary, the correct present value should be approximately 7,269.57, and the provided answer 7,268.12 is not precisely correct given standard present-value calculation with a 3.5% annual discount rate. The discrepancy is about 1.45, which is a small difference likely due to rounding choices.

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If the future value in one year is $7,524 and the discount rate is 0.035, what is the current price?

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