Case(rate)

The first part of the Student Loan app is quite sane: looking into a loan situation from a clear perspective: how many payments would I have to make, how much would I still owe at time t.The second part is more of an after-the fact perspective. One is deep into it, and wondering when it will all end.

We will be considering two situations, working with, in both cases, amount of interest paid in one year, and amount of monthly payment

The two elements that give structure to a loan are: rate of interest, and number of payments. At the end of the day, interchangeable. Let us see what happens if we know interest rate.
With our example: I know that I have paid 5.32$ in interest in the last year, and made payments of 8.77$ per month. Adding to the mix that the interest rate was 5%, I will calculate for the interest amount for n =12. (Remember that the n(s) are moving backward in time from the point of view of amortization).

(1 - (1/1.004167^12))* 8.77 = .43

I then subtract the ln for power11, from ln power12, and convert to money, to get approximately .04.

This is the amount of change in interest payment from one month to the other. Now I need to locate the series which gives me 5.32$

Here is where the real programming begins; in pseudo-code:
-Create an array of 24
-Populate it with 4, 4+4, 4+ 4 + 4 etc
-Create a function that checks for a series of 12 that add up to 5.32
-Report the position in the array
Substract 1.That is how many payments of 8,77$ are still due.
Some programs give a balloon number at this point: how much is due if one merely pays
off the capital.