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.