Question

Greater compounding frequency will result in a larger present value.

True or false

Answer 1

This statement is False.

Greater compounding frequency will result in smaller positive value.

Let's understand this with the help of an example

Robert Downey Jr. will be getting $9,000,000 in a year. If the rate of interest is 12% compounded annually, the present value of the money he will be getting in a year shall be:

It means that the value of $9,000,000 to be received today is $8,035,714.29

Now, Lets see if Robert gets the same amount but the interest rates are compounded monthly. The present value shall be:

As we can see, when compounding frequency was greater (in second case), the PV value is actually less. It is $7,987,043.027 as compared to $8,035,714.29.

This is happening since the denominator(it is 1.126825) is rising in the second case as compared to first case(1.12).