With an applicable annual interest rate of 10%, what is the present value of a $500,000 lump sum that will be received in 14 years?

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BlackTom AI · Accepted Answer

First, identify what is being asked: the present value (PV) of a future lump-sum of 500,000 to be received in 14 years, using an annual interest rate of 10%. The standard PV formula is PV = Future Value / (1 + r)^n, where r is the rate and n is the number of periods.
Option A: $132,612.42 — this would imply a denominator (1.10)^14 that is slightly smaller than what is actually required, yielding a PV a bit higher than the correct value. Since the correct PV is approximately $131.7k, this is too large.
Option B: $131,665.63 — this aligns closely with the precise calculation of 500,000 / (1.10)^14. Given (1.10)^14 ≈ 3.7975, 500,000 / 3.7975 ≈ 131,665.63, so this is the accurate PV.
Option C: $130,985.61 — this is somewhat smaller than the precise value, which would occur if (1.10)^14 were larger than 3.7975 or if rounding pushed the PV downward; however, the difference here is due to an overestimation of the discount factor, making PV too low.
Option D: $126,771.36 — this is noticeably too low, suggesting a discount factor far larger than (1.10)^14 or a much larger n, which is inconsistent with the given 14-year horizon and 10% rate.

In summary, the present value calculation uses PV = 500,000 / (1.10)^14, which evaluates to approximately 131,665.63. The other options deviate from this value due to incorrect discounting or misestimation of the growth factor, reflecting common calculation or rounding errors rather than correct applications of the formula.

BUSFIN 3220 AU2025 (2910) Trial Exam 1 - Requires Respondus LockDown Browser

With an applicable annual interest rate of 10%, what is the present value of a $500,000 lump sum that will be received in 14 years?

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