## Question

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

a) 6 percent interest for 5 years

b)6 percent interest for 8 years

c) 6 percent interest for 10 years

d) 8 percent Interest for 5 years

e) 8 percent interest for 10 years

## Explanation

To determine which of the given options will produce the lowest present value interest factor (PVIF), we need to understand what a PVIF is and how it is calculated.

A Present Value Interest Factor (PVIF) is a factor used in financial calculations to find the present value of a future cash flow. It’s calculated using the formula:

PVIF = 1 / (1 + r)^n

Where:

- PVIF is the present value interest factor.
- r is the interest rate per period.
- n is the number of periods.

In this case, we are given two interest rates (6 percent and 8 percent) and three different time periods (5, 8, and 10 years). We need to calculate the PVIF for each option and see which one produces the lowest value. Lower PVIF indicates a lower present value, which means less value in today’s terms.

Let’s calculate the PVIF for each option:

a) 6 percent interest for 5 years: PVIF_a = 1 / (1 + 0.06)^5

b) 6 percent interest for 8 years: PVIF_b = 1 / (1 + 0.06)^8

c) 6 percent interest for 10 years: PVIF_c = 1 / (1 + 0.06)^10

d) 8 percent interest for 5 years: PVIF_d = 1 / (1 + 0.08)^5

e) 8 percent interest for 10 years: PVIF_e = 1 / (1 + 0.08)^10

Now, let’s calculate these values:

a) PVIF_a ≈ 0.7473 b) PVIF_b ≈ 0.7118 c) PVIF_c ≈ 0.5584 d) PVIF_d ≈ 0.6806 e) PVIF_e ≈ 0.4632

Comparing these values, we can see that the lowest present value interest factor is for option (e) – “8 percent interest for 10 years.” So, option (e) will produce the lowest PVIF among the given choices.

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