APR Monthly Calculation

[maudise]

Hi All,First, apologies if this is in the wrong forum, let me know and I'll happily put it elsewhere. Second, this is going to be quite lengthy as I try and give the detail behind the problem.The problem is simple to say, but difficult to work out once all the factors have been accounted for (in my mind).

The statement; We want to charge 20% APR on all credit agreements regardless of length, and we'll take payments monthly.

The question: What's the formula to work out the monthly payments required for this formula.

It should be stated at this point, I can use excel to get me my flat rate equivalent answers, however I need to understand the formulas behind it should it ever need expanding.So, the APR is not the nominal interest rate found in excel (which would make this infinitely easier), it is in fact from the OFT which states that the APR should be (1 + r) ^m - 1 where r = Internal Rate of Return and M is payments.The IRR formula requires a regular payment figure, but from what I can see it is a 'guess and check' calculation?

IRR = WHERE FV = 0, PV = FV / (1 + r)^m where 
PV = value of amount loaned (£500 is input as -£500), 
r is the Interest Rate and m is number of years

I rearranged that to

r =[(PV/FV)^1/m - 1 ] (pv/Fv)^-1/n

which is a problem when you're trying to solve for FV = 0 as you cannot divide by 0. So, How do I get from an APR of the function

APR = (1 + r)^m -1 where APR is 0.2, r is the 
Internal Rate of Return and m is the number of years

to a monthly repayment amount? Note; we cannot use PMT function in excel as it gives the nominal interest rate rather than the prescribed APR calculation.Any help would be greatly appreciated. Maudise

Edit: Apologies for the format, it doesn't seem to like to make a new paragraph. I've done my best with code tags

 

[maudise]

Hi Dennis,Here in lies my problem. The APR is as defined by the Office of Fair Trading which is;

i = (1 + r)^M - 1where i = APR; r = internal rate of return; m is years

It's difficult to explain, but the idea is how to rearrange the formula to get the payment for a set APR using the formula above. The formula for IRR is as follows;

PV = FV (1 + r)^mwhere PV = value of advance; FV = 0; r = flat interest rate, n number of years

What I've discovered from all of this is that APR / Interest is massively more complex than it would seem, and the attempts to simplify it for the consumer are frighteningly bad!ThanksMaudise

 

[maudise]

Thanks very much.