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Old 10-12-2012, 07:44 PM
NWO NWO is offline
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Join Date: Oct 2012
Posts: 2
Default Basic Annuity Valuation

Hi Everybody,

Here is a very simple problem that I can't solve for some reason.

The Question says that you will receive $500K semiannualy with an interest rate of 0,05. R=0,05 here is the annual rate so we need to find the semi-annual rate first before we go on. R/2=0,025.

The basic PV calculation for 4 periods yields an answer of $1,939,394.

PV> 500K/(1,025)^(0,5) + 500K/(1,025)^(1) + 500K/(1,025)^(1,5) +500K/(1,025)^(2)= $1,939,394.

This is ok and I understand it but when I put this into Annuity formula I dont get the same result for some reason.

My annuity formula is as follows;

PV(Annuity)= (500K/0,025)*[1-1/(1,025)^(4)]= $1,880,987

In Annuity formula above, I just thought that we have 2 periods in a year since we will get paid semi-annually and for 2 years, so this means we have in total 4 periods.

Where is the flaw here and why doesnt it yield the same result as simple discounting?

Thanks in advance
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Old 10-13-2012, 09:39 AM
ArcSine ArcSine is offline
Join Date: Oct 2010
Location: North Carolina, USA
Posts: 89
Default Re: Basic Annuity Valuation

Since you're correctly expressing everything in terms of 6-month periods, then 2.5% is the rate per period (as you're using) but also each 6-month period is one whole period.

Hence you have 4 "whole" periods, each one of 6 months, and your simple discounting should be...

500 / 1.025^1 +
500 / 1.025^2 +
500 / 1.025^3 +
500 / 1.025^4

Make that simple change and you'll be back on track.
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Old 10-13-2012, 11:14 AM
NWO NWO is offline
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Join Date: Oct 2012
Posts: 2
Default Re: Basic Annuity Valuation

Thank you for your reply. I appreciate it. Then I guess the book has a problem because it shows that the annual interest rate is adjusted accordingly for semi annual compounding but they forgot to adjust the top right?
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