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October 7th, 2008, 11:41 AM   #1
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Present Value of An Annuity

Hello. I have been banging my head on the wall with this problem and would appreciate some help.

I know the general formula for calculating the present value of an annuity (due or ordinary) can be found here:
http://www.getobjects.com/Components...e/TVM/pva.html and I completely understand everything on that page which is assuming that interest is compounded monthly.
Where I run into trouble is to change the assumption that interest is compounded, say, daily. I would think it is as easy as saying i = rate/365 and n = number_of_years * 365. However, using those numbers the formula does not work out to a realistic answer.

Can somebody help? Thanks!
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October 7th, 2008, 04:04 PM   #2
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Re: Present Value of An Annuity

The numbers don't work out because you're not just calculating interest at each period, you're also getting annuity payments. Getting paid (the full monthly amount) daily is quite a change!

Instead, just figure out the effective monthly interest rate and use it instead of the daily compounded rate.

4% interest compounded daily gives a yearly interest rate of (1 + r/n)^n - 1 = 4.08%; to get this rate by compounding monthly you'll need to solve

1.0408 = (1 + r/12)^12

which gives r = 4.006%.
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October 8th, 2008, 10:58 AM   #3
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Re: Present Value of An Annuity

Thanks for your help. I now know why I was getting those crazy numbers. Can you help me out with a couple of examples? I am coming within a couple of dollars of the answers that appear on this website and I am not sure why I am not getting the exact numbers using the formula from my first post with your effective daily compounded rate. Thanks!

In each example they are using daily compounding but the withdrawal rate is changing:

http://www.timevalue.com/timevalueca...&PostBack=true
http://www.timevalue.com/timevalueca...&PostBack=true
http://www.timevalue.com/timevalueca...&PostBack=true
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October 8th, 2008, 12:41 PM   #4
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Re: Present Value of An Annuity

The site may be calculating based on differing lengths of months, I don't know.
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