# Thread: Calculating the actual cost of a loan

1. ## Calculating the actual cost of a loan

Hey guys, got a math problem here. Teacher didn't give us anything on how to do it, and algebra was years ago. Here is the problem:

The first month he pays 1.65% of 650= $10.73 (rounded up to the nearest penny) interest so he actually paid 21.45- 10.73=$10.73 toward the principle, leaving 650- 10.73= 639.27 still to be paid. The second month he paid 1.65% of 639.27= $10.55 interest so he actually paid 21.45- 10.55=$10.90 toward the principle leaving 639.27- 10.90= $628.37 still to be paid. The third month he paid 1.65% of 628.37=$10.37 interest so he actually paid 21.45- 10.37= $11.08 toward the principle leaving 628.37- 11.08= 617.29 still to be paid. Continue that until the principle is paid off. Question 1: How long will it take him to pay for the stereo? Question 2: What is the total amount Dimitri will pay for the stereo? Question 3: What is Dimitri's total cost of using credit? I have no idea where to even start. Thanks. 3. ## Re: Calculating the actual cost of a loan Originally Posted by HeyAwesomePeople "Dimitri wants to buy a stereo for 650 dollars and pay for it using a credit card that has an Annual Percentage Rate of 19.8% and a periodic interest rate of 1.65%. Dimitri pays a minimum monthly payment of$21.45"
Formula for loan payment calculation:
p = a*i / [1 - 1/(1+i)^n]
p = 21.45
a = 650.00
i = .0165
n = ?

In terms of n, formula becomes:
n = LOG[p / (p - a*i)] / LOG(1 + i)

Do the maths and you'll find that when n=42,
7.52 remains owing; so a small 43rd payment remains.

If payment was 21.58, then n=42 would result in zero owing.

If you're still stuck, then you need classroom help:
not provided here.