## Tuesday, December 18, 2012

### Loan Payments And APR

So I've been working on a few loan pieces recently and I keep needing to re-find the formulas so here's a place for me to put the things I find.

## Calculating Payments

Interest Rate(r) = 13.5%
Periods Per Year(p) = 52 (compounding weekly)
Number of payments(n) = 157 (weeks)
Loan Amount(PV) = \$12000

The Excel Way: `=PMT(r/p, n, PV) (reference)`
The Mathematical Way: `r(PV) / [1 - (1+r)^-n]`
The Java Way:

## Calculating APR

Assuming the above, plus a Payment Amount(a) = \$93.16

The Excel Way: `=RATE(n, a, PV) * p` (reference)
A Mathematical Way: ` [(Interest payments + fees)/number of years] / Average amount borrowed*` (reference)
*In the reference site notice how they calculate the average borrowed.
The Java Way:
I have found there are a lot of ways of how to calculate APR floating around and none of them are very straight forward.

And even understanding the FDIC's rules on it can be a little hairy. My take is that you have to get it right to within .25% or .125% of however the FDIC calculates it, depending on the type of loan.

Here is an Excel Sheet with the Payment and APR formulas.