Question

Buford pays for a $4000.00 vacation with a credit card that has a 20% APR. He decides to make $200.00 monthly payments.

What is the total amount of interest and fees based on the APR?

Answer 1

So clearly we don't know how many payments there are,
let there be n payments
i = .20/12 = .01666...
4000 = 200(1 - 1.016666..^-n)/.016666..
1/3 = 1 - 1.016666..^-n
1.01666..^-n = 2/3
take log of both sides, and use log rules
-n log 1.01666... = log (2/3)
-n = -24.53..

So he has to make 24 full payments and a partial payment
so he paid appr 24.5($200) or $4906 for his loan

Btw, to simply multiply the $200 by the number of payments is an invalid
actuarial math calculation, since it neglects the "time" passed between payments.
remember, the old saying, "time is money"
e.g. If I paid you $200 now or if I paid you $200 2 years from now would not be
equivalent.