Which one of the following will produce the lowest present value interest factor?

Question

BlackTom AI · Accepted Answer

Present value interest factor (PVIF) is given by PVIF = 1 / (1 + r)^n. Because the denominator (1 + r)^n grows as the interest rate r or the number of periods n increases, PVIF decreases when r or n increases. Thus the lowest PVIF comes from the largest combination of rate and periods.

Step-by-step computation for each option (showing intermediate steps):

A. 6% for 5 years:
(1 + r)^n = 1.06^5 = 1.3382255776
PVIF = 1 / 1.3382255776 ≈ 0.74726

B. 6% for 8 years:
1.06^8 = (1.06^4)^2; 1.06^4 = 1.26247696 → 1.06^8 ≈ 1.593848
PVIF = 1 / 1.593848 ≈ 0.62741

C. 6% for 10 years:
1.06^10 = (1.06^5)^2; 1.06^5 = 1.3382255776 → 1.06^10 ≈ 1.7908477
PVIF = 1 / 1.7908477 ≈ 0.55840

D. 8% for 10 years:
1.08^10; 1.08^5 ≈ 1.469328 → 1.08^10 ≈ 2.158925
PVIF = 1 / 2.158925 ≈ 0.46319

Comparison: PVIFs are A ≈ 0.7473, B ≈ 0.6274, C ≈ 0.5584, D ≈ 0.4632. The smallest (lowest) PVIF is option D.

Why D is correct: it combines both a higher interest rate (8% vs. 6%) and the longest term shown (10 years), producing the largest denominator (1 + r)^n and therefore the smallest PVIF.

Why the other options are incorrect: A and B have shorter terms (5 and 8 years) at the lower 6% rate, so their denominators are smaller and PVIFs larger. C has the same 10-year term but the lower 6% rate, yielding a larger PVIF than D.

Conclusion: The lowest present value interest factor is D. 8 percent interest for 10 years, matching the provided answer.

Which one of the following will produce the lowest present value interest factor?单项选择题

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