PV of Perpetuity Required for Indefinite PMTs continue, question, current

TheMBAGlover

Hi all,

Got a question on a mock and I couldn't figure out why N=3 instead of N=4. Jist of question is as follows:

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Scholarship fund wants to pay out a $25,000 scholarship annually indefintely. The fund will begin paying the scholarship at the end of 4 years and will be able to return 4% compounded semi-annually.

What is the current amount that must be deposited today to ensure this can continue indefinitely?

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So I solved it as follows:

4% EAR = ((1+(.04/2))^2 = 4.04%

FV = (25,000 / .0404) = $618,811.11

Discount that back to the PV that must be deposited to ensure $25,000 is available every year. This is where I go wrong.

The payment is an annuity, NOT an annuity due, so why is the answer N=3 and not N=4?

I discount back to N=4 for a PV of $528,149.98. However, the answer is N=3, PV = $549,487.24.

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Simple question then. If the PMT isn't required until the end of the 4th year, why are we only discounting it 3 years? Are all PV perpetuities solved for a PV of (N - 1)?

amqata

I know I am way behind this post but I had a hard time wrapping my head around this rule as well. If you are using your calculator would you leave it in END mode? I worked it with n=4 in begin mode originally.

ramzes

I know I am way behind this post but I had a hard time wrapping my head around this rule as well. If you are using your calculator would you leave it in END mode? I worked it with n=4 in begin mode originally.

thanks!

ajpheif16

Yeah, you will first calculate the perpetuity value and then use n = 3 to discount it in END mode...