Problem 24E

a) Find a recurrence relation for the balance B(k) owed at the end of k months on a loan at a rate of r if a payment P is made on the loan each month. [Hint: Express B(k) in terms of B(k — 1) and note that the monthly interest rate is r/12.]

b) Determine what the monthly payment P should be so that the loan is paid off after T months.

SOLUTION

Step 1

In this problem we are asked to find a recurrence relation for the balance .

Therefore