You are planning to buy a new home. The house costs $300,000, but you only have $25,000 in savings that you can use as down-payment. The remainder needs to be financed by a mortgage. Your bank offers a 25-year loan, with fixed annual interest at 7.5, and fixed monthly payments.
1. What are the monthly payments that you have to make for the entire mortgage to be paid off in 25 years?
2. If you can afford to pay at maximum $2,000 per month, can you afford the house? If not, how much additional down-payment would it be required?
3. Now suppose you pay $2,400 per month instead. Can you pay off the mortgage in 20 years without having to increase your down-payment?
4. The bank also offers an “interest-only” mortgage, again at 7.5% fixed annual interest. If you go for this solution, you would have to make fixed monthly payments, part of which go to the mortgage lender as interest, while whatever is left would be deposited in a fund that earns interest at rate “R”, compounded monthly.
Assume that you maintain the $25,000 down-payment. Consider different scenarios: monthly payments of $2,000 or $2,400, and length of 20 or 25 years for the loan. For each combination (there are 4), work out the minimum rate of return “R” that you must earn on your deposits so that you will be able to pay off the debt at the end of the contract’s lifetime.