I need help with this math problem?

Question

it one of those intrest formula problems.
if you have a principle of 30,000 and an APR of 15%, the person is going to pay it back in weekly installments of 250 dollars, how long does it take to pay back the loan, how did you figure this and what formula? thanks! do they add the intrest every week? how does this work?

Answer 1

147 weeks or 2.84 years.

In Excel the formula is
=NPER(15%/52,250,-30000,0)

The interest is divided into a weekly amount, and then calculated every week because the principal amount is changing.

Answer 2

Use a financial calculator, either hand-held or on-line. Enter your knowns: PV=30,000, FV=0, pmt=250, i=15%/52, and then solve for n, which equals 148. (note: PV is present value, FV is future value, pmt is payment, i is interest, and n is number of periods). So it will take 148 weeks, or a little over 2 years and 10 months, to pay back the loan.

I've compounded weekly. You could complicate this a little more by compounding monthly, or daily, but still having payments made weekly. In actuality, a lot of lenders would accept weekly payments but only post it to the account monthly. But I believe the question's intent is to solve as I have above. Hope that helps.