Question

Which one of the following will increase the present value of a lump sum future amount? Assume the interest rate is a positive value and all interest is reinvested.
A. Increase time period
B. None of these
C.Increase in interest rate
D. Decrease in time period

Double checking, I believe answer is C.?

Answer 1

The correct answer to the above question is D. (Decrease in time period). The formula for calculation of present value of a future amount is as follows:

Present Value = Future Value * 1 / (1+i)ⁿ

Here, i = interest rate in decimal

and n = time period.

This problem can be solved with an example, Lets assume that future value or the amount that will be received in future is $10,000 with interest rate of 5% and time period of 5 years. The present value for the same will be

PV = $10,000 * 1 / (1+i)ⁿ

       ⁼ $10,000 * 1 / (1+0.05)⁵

      ⁼ $10,000 * 1 / 1.27628

    = $10,000 * 0.7835

    = $7,835

and if we reduce the period to 3 years, let us see the change in present value

= $10,000 * 1 / (1+i)ⁿ

= $10,000 * 1 / (1+0.05)³

=$10,000 * 1 / 1.157

= $10,000 * 0.8643

= $8,643

Hence, if the time period is reduced from 5 years to 3 years, the present value of a future amount will increase.