Calculate payments based on APR

[Robert T. Repko (R Squared Consultants)]

Believe it or not at 4/14/2009 10:11 AM, Kenneth Brody said:
>Robert T. Repko (R Squared Consultants) wrote:
>>Believe it or not at 4/13/2009 08:23 PM, Kenneth Brody said:
>[... 365 daily payments vs 12 monthly payments ...]
>>That's what I thought but when I ran it my answer was different by 
>>.315/month, 89.74 vs. 89.425
>[...]
>>eh = TVM_PMT(pi,ep,ez,"0") = $2.94 daily payment
>>"2.94" * "365" / "12" = 89.425
>>2.94 is daily payment, mult. by 365 for annual payment, divide by 
>>12 for monthly payment = 89.425.  That's a difference of ~ 
>>$.315/month.  Maybe I'm wrong but I wouldn't expect that much 
>>difference between daily vs. monthly calculations, and I would 
>>expect the daily calculations to be higher than the monthly 
>>calculations not lower.
>
>Why would you expect to pay more if you pay it faster?  (And the 
>difference is about 1/3 of 1%.)
>
>Try a different angle, and you'll see this is correct.
>
>You agree that 12 monthly payments on $1,000 at 13.9% was 89.74 
>each, correct?  (That's what filePro and your calculator both came up with.)
>
>That's a total of $1076.88 in payments.  However, if you were to 
>make a single yearly payment, you would pay $1139.00, correct?  By 
>paying it in more payments over the same time, the total payment is less.
>
>So, making 365 daily payments of $2.94 instead of 12 monthly 
>payments of $89.74 means you pay a total of $1073.10, for a whopping 
>$3.78 savings.
>
>--
>Kenneth Brody

First let me say thank you for working with me on this Ken, I really 
do appreciate it and I hope I don't sound argumentative because I am not.

The difference might be small but I didn't expect that much of a 
difference and the difference to be the opposite of what I 
expected.  I could be wrong but my concern is using this in 
production and I found out the hard way my calculations are wrong.

Lending institutions calculate compound interest on a daily basis 
instead of monthly basis for one reason they make more money on interest.

If I compound on a daily basis the interest is compounded 30 times by 
the end of the month instead of once if it compounded monthly.

If I pay the 1000.00 loan off on day 1 I pay 1002.94.  If I don't 
make a payment on day 1 but pay if off on day 2 I pay 1005.88.  The 
longer I wait to pay the more I pay in interest which makes my 
payments higher.  If I pay monthly the I will pay more if the 
calculation are done on a daily basis vs monthly basis.  If I quote a 
monthly payment I expect the payments to be higher if I compound 
daily vs monthly.