# Math Help - Stranger loan

1. ## Stranger loan

AcmeCard works like this:
monthly payments = fixed percentage of balance owing before interest is added,
with minimum payment specified; interest is charged monthly.

Example: $1000 owing, payment = 7% of balance owing, mimimum payment =$50, interest 1% per month.

Month1: 1000.00 - 70.00 + 10.00 = 940.00
Month2: 940.00 - 65.80 + 9.40 = 883.60

Month6 ends with ~689.87 owing; minimum payment starts in month7, since 689.87 * .07 = ~48.29

Month20 will end at ~45.62, lesser than minimum payment of 50.
So FINAL payment will be in month21, for 45.62(1.01) = ~46.08

Clear nuff?

OK:
a = original amount owing (1000 in above)
i = monthly interest factor (.01 in above)
p = percent of balance factor (.07 in above)
m = minimum payment (50 in above)

As a "general case", what is the FINAL payment in terms of a,i,p,m ?

Of course, it is assumed that at least the 1st payment is higher than the minimum payment.
In other words, ap > m.