Question

Loans in general operate using compound interest. Every fixed amount of time (usually a month) a payment is made and this is de- ducted from the remaining debt. An interest rate is then applied to the debt, and the pro- cess continues until the debt is cleared out.

1. If you take a loan for a new $20,000 car, a typical APR with a fair credit score is 4.8% interest. If you make monthly pay- ments of A dollars, find an expression for your debt right after your first payment.

2. How much debt is left right after the sec- ond payment?

3. Find a sequence dn that gives the re- maining debt right after the nth month.

4. Find your monthly payment A if you want to pay your loan in 5 years.

5. How much total interest would you pay for the car?

Answer 1

1. New Car loan $20,000 - Interest rate 4.8%

Remaining debt after first payment = $20,000 * 4.8% = 960

Therefore remaining debt would be = $20,000 - $ 960 = $ 19,040

2. Debt left after sec - ond payment = $19040 - ($19,040 *4.8%)

= $18126.08

4.Monthly payment A to pay off the loan in 5 years would be = $4048

5.Total Interest paid for the car would be = $ 241