Calculating APR - Regulation Z Appendix J

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MortgageGirl

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Hello!

I'm a programmer, and I'd like to calculate the APR in my application. I'm trying to understand the formulas outlined in http://ecfr.gpoaccess.gov/cgi/t/text/te ... 18&idno=12. I've seen it reworked (http://members.aol.com/stevef88/discuss/apr.htm - I found this from a search on this message board; thank you):

P = (A-F)*r/[1 - (1+r)-N]

I'd also like to include odd days interest when applicable (I've seen it as A=[1/(1+fi)(1+i)^t][?not sure what goes here?] - how would that be incorporated into the equation above? I understand how to calculate APR in excel using the RATE or IRR function, but I'm trying to understand how to actually loop through the iteration by hand (well in code really), including the odd days interest. I may also have uneven payment flows at different interest rates (for ARM mortgages)…

I have the rate, payment schedule, loan amount & fees available to plug into the equation; I understand parts of the equation but I just can't figure out how to put it all together. What is the equation solving for...what needs to loop...what numbers to plug in & where....ect....

Does anyone know where I could get more information? I've read Reg Z appendix j about 3 times & just get more confused….any help is appreciated!!!

Thanks for your time,
Sarah
 
I don't think this is the right forum for this. Perhaps you should go and see a bank in person for the best advice.
 
Solving for interest rates often is not possible with a closed-form solution. Estimation is the way to go, followed by iteration.

In what environment are you programming?

Are you being asked to do this with no background in such things?
 
Thanks for your reply. I'm programming in vb.net...I have mortgage experience; however I'm not too familiar w/many financial formulas.

So when you guess, what are you trying to equal? What should be iterated? Is this how the IRR function works? It would be great if I could find a breakdown of how this function works; I’ve searched the web but can’t find anything…
 
Just to get an idea of where you're at:

what is the MONTHLY payment on a $300,000 mortgage, over 25 years,
at an interest rate of 8% compounded ANNUALLY ?
 
I actually have the entire payment schedule...it would be more like:

what is the APR for a $20,000 loan w/12 pmts of $1712.15; interest rate of 5%...

Also, this would include 10 days of odd day's interest at a rate of 2.7778 per day, a total of $27.78. This interest affects the APR and results in a longer 1st payment period...

Thanks!
 
MortgageGirl said:
I actually have the entire payment schedule...it would be more like:
what is the APR for a $20,000 loan w/12 pmts of $1712.15; interest rate of 5%...
Also, this would include 10 days of odd day's interest at a rate of 2.7778 per day, a total of $27.78. This interest affects the APR and results in a longer 1st payment period...
Click to expand...

You're side-stepping my question; can you answer it ?
Just trying to make sure you're not learning to fly a jet
before learning how to bring out the wheels before landing!

And on your example:
sure, 1712.15 is the required monthly payment to repay 20,000 over
12 months, at a rate of 5% compounded MONTHLY;
that's an APR of 5.116~% : (1 + .05/12)^12 - 1

WHY do you say that the 27.78 affects the APR?
APR is Annual Percentage Rate, right?

Up here in Canada, your example would be handled this way:
"please remit post-dated cheque for 27.78 as interest adjustment" :wink:
 
Ha! Fair enough - I depend on the built in computer functions too much; that's why I'm completely lost:

So using your example, I take the 8% to .08 & divide by 12 to get the annual rate. Then:

300000 * (0.00666666667 * ((1 + 0.00666666667)^300))/((1 + 0.00666666667)^300 - 1)

So the mo pmt would be $2,315.45 (rounded up). Is that right?

I would LOVE to exclude the odd days interest, however under Reg Z you're required to add it in & can't be more then 1/4th or 1/8th of a percent off (depending on the loan type) - at least from what I understand. Reg z uses fractional interest to calculate this (an iteration method); something like:

(1+fi)(1+i) where f is 10 days/30 days in a month.
 
MortgageGirl said:
So the mo pmt would be $2,315.45 (rounded up). Is that right?
Click to expand...

No.
2260.25 (rounded) is the correct payment.
You need to use rate of 7.72~% in your calculations.
7.72 compounded MONTHLY = 8.00 compounded ANNUALLY.

Perhaps you should make sure of the basics before attempting
this complicated stuff...just trying to be helpful...
 
Getting back to this:
"what is the APR for a $20,000 loan w/12 pmts of $1712.15; interest rate of 5%...
Also, this would include 10 days of odd day's interest at a rate of 2.7778 per day, a total of $27.78. This interest affects the APR and results in a longer 1st payment period... "

All this means is the loan was "ready" 10 days before a payment date;
interest of 27.78 has been earned by the lender before the theoretical
contract date; it is the same as the borrower borrowing another 27.78
10 days later; loan is then:
20, 027.78 with 12 monthly payments of 1714.53 at rate of 5%.

No matter how you cook it, the 27.78 is "borrowed" by the borrower,since
the borrower does not pay it back 10 days later. It can be "called" anything
that turns bankers on...but it is an amount that is financed...
 
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