Buy a new car $10000 with an installment plan, you will pay a fixed monthly repayment for 24 months period. and the annual interest rate is 5.9% compounded monthly.

Let S0 be the initial money owes = $10000

Let Sn be the amount of money that still owes the shop at end of the n month, following the n payment.

Let R be the monthly repayment.

You start to repay at the end of the first month and completely settle all the payments at the end of the 24 month.

1. Write down a recurrence relation for S1,S2,S3 in term of R.

2. Propose a recurrence relation to express Sn in terms of Sn-1 and R.

3. Use the method of undetermined coefficients to your proposed relation in (2) to find an explicit formula for Sn in terms of R.

4. Find the monthly repayment R.

5. What is the total interest?