Question

find a recurrence relation for the amount of money outstanding on a $30,000 mortgage after n years if the interest rate is 8 percent and the yearly payment (paid at the end of each year after interest is computed) is $3,000.

Answer 1

We can use this recurrence relation to calculate the amount of money outstanding on the mortgage after any given number of years, starting from the initial amount of $30,000.

Explanation:

Let's denote the amount of money outstanding on the mortgage after n years as M(n). Here's how we can establish a recurrence relation based on the given information:

In each year, the remaining balance on the mortgage will accrue interest at a rate of 8 percent. Therefore, the interest accrued in year n will be 8 percent of the amount outstanding at the end of year n-1.

The yearly payment of $3,000 will be subtracted from the outstanding balance at the end of each year.

So, the recurrence relation for the amount of money outstanding on the mortgage after n years can be expressed as:

M(n) = (1 + 0.08) * M(n-1) - 3000

Here, (1 + 0.08) represents the 8 percent interest rate, and M(n-1) denotes the amount of money outstanding at the end of the previous year.

We can use this recurrence relation to calculate the amount of money outstanding on the mortgage after any given number of years, starting from the initial amount of $30,000.