QuestionJune 2, 2025

How would a decrease in the interest rate effect the present value of a lump sum, single amount problem (all other variables remain the same)? Multiple Choice Increase the time needed to save. Increase the present value. Change the future value. Decrease the present value.

How would a decrease in the interest rate effect the present value of a lump sum, single amount problem (all other variables remain the same)? Multiple Choice Increase the time needed to save. Increase the present value. Change the future value. Decrease the present value.
How would a decrease in the interest rate effect the present value of a lump sum, single amount problem (all other variables remain the same)?
Multiple Choice
Increase the time needed to save.
Increase the present value.
Change the future value.
Decrease the present value.

Solution
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Answer

Increase the present value. Explanation 1. Understand the relationship The present value (PV) of a lump sum is calculated using the formula **PV = \frac{FV}{(1 + r)^n}**, where FV is the future value, r is the interest rate, and n is the number of periods. 2. Analyze the effect of decreasing interest rate A decrease in the interest rate r will increase the denominator (1 + r)^n, thus increasing the present value PV when all other variables remain constant.

Explanation

1. Understand the relationship<br /> The present value (PV) of a lump sum is calculated using the formula **$PV = \frac{FV}{(1 + r)^n}$**, where $FV$ is the future value, $r$ is the interest rate, and $n$ is the number of periods.<br /><br />2. Analyze the effect of decreasing interest rate<br /> A decrease in the interest rate $r$ will increase the denominator $(1 + r)^n$, thus increasing the present value $PV$ when all other variables remain constant.
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