You have saved \$40,000 for a deposit on a home purchase. A cheerful Victorian home is on sale for \$370,000. You have qualified for a home loan mortgage at an annual interest rate of 3.6% compounded monthly. You plan on paying off the home loan with a monthly mortgage payment of $1600.
Write a recurrence relation that models how your loan balance changes from month to month. Round all numbers to three decimal places.
I have no idea how to approach this problem. Any help would be appreciated.
At least in the United States, interest is applied to your outstanding balance at the end of each month and you are expected make a monthly payment. Lets call the outstanding balance after n months Bn, the monthly interest rate R and the monthly payment M. At the end of month n, you would have accrued Bn*R interest and would make a payment of M, so your balance Bn+1 would be (1+R)*Bn - M.
The monthly rate of interest is simply the yearly rate divided by 12, we work with calender months, so February's interest is the same as December'.
I'm not sure how your downpayment (D) fits in, I guess you subtract that from the house price to start B0, the first term in the sequence.
Can you work it out from there?
