4.11 Mortgages I
Student Notes
Unit 4: Financial Math MHF4U1: Advanced Functions
Terms Mortgage: a loan, which is an agreement between a money lender and a borrower to finance a purchase. The loan is repaid in equal payments at equal time intervals, with payments that include both principal and interest. to amortize a mortgage means to repay the mortgage over a given period of time (the amortization period) in equal payments at regular intervals. Common amortization periods are 15, 20 and 25 years. length of time the mortgage agreement is in effect (most mortgages have 3, 4 or 5 year terms). Once the term is up, the mortgage is usually renegotiated (ie. interest rate) a table that follows the progress of the mortgage by showing how much of the principal remains after each payment. require that people who take mortgages pay a percent of the purchase price immediately. Down payments are often 20% of the purchase price of the house. a mortgage where the interest is compounded semi-annually
Amortization:
Term:
Amortization Table: down payment
Canadian Mortgage
Problems Calculating Mortgages-Equivalent Rates Calculate the monthly rate for a $120,000 mortgage amortized for 20 years at 6.2%/a compounded semi-annually (from now on assume mortgages are compounded semiannually). What is the problem? Monthly payments but semi-annual compounds. We must find an equivalent interest rate. (1 + i)12 = (1 + 0.062/2)2
Example 1) Calculate the equivalent rate for each payment schedule. We are using Canadian mortgages where the interest is compound semi-annually: a) 3.4%/a for a bi-weekly b) 7.8%/a for a monthly c) 6.5%/a for a daily payment payment payment
Calculating Payments and Interest Example 2) Using the present value of an annuity, calculate the monthly payments for the example above.
Example 3) Find the total interest you will pay for 20 years.
Example 4) If you amortize your mortgage for 25 years how much interest would you pay?
Example 5) Jamie wants to buy a house that is worth $250, 000. He can put down 10% of the value of the house. If Bank of Attanasio offers 5%/a mortgage amortized for 25, what would Jamie’s monthly payment be?
Problem 1 Dana buys a home. She needs a mortgage of $100 000. The bank offers Dana a 25-year mortgage at 8.5%. What is the monthly payment? **From now on, we should automatically assume a mortgage is compounded semi-annually, with payments made monthly. Therefore, Dana’s mortgage is a 25-year mortgage at 8.5%/a compounded semi-annually. Use the TVM Solver to find Dana’s monthly payments. Fill in your missing information… N ____________________________ I% ____________________________ PV _________________________ PMT ____________________________ FV ____________________________ P/Y ____________________________ C/Y ____________________________ LWhat is Dana’s monthly payment?
LWhat is Dana’s new monthly interest rate? (follow the previous example for this…remember to find the future value of $1 for one month)