1 SS Mortgages MCR3U – Mr. Santowski

2 (A) Terms Related to Mortgages a mortgage is special loan that is repaid over a longer period of time the amortization period refers to the length of time that you have to repay the mortgage the stated interest rates for mortgages (say 6%) means that the compounding period is semi-annual so if you make monthly payments, then our payment schedule is not the same as the compounding period ==> hence we get into a concept called equivalent rates

3 (B) Equivalent Rates two interest rates are equivalent if they yield the same amounts at the end of one year (or at the end of any number of years) ex. You invest $1 in an account that earns 10% compounded semi-annually. Likewise, you invest $1 in an account that compounds the interest monthly. If the two future values are to be the same in half a year, determine the interest rate in the second investment.

4 (B) Equivalent Rates Investment #1 A = P(1 + i) n A = 1( ) 1 A = $1.05 Investment #2 A = P(1 + i) n 1.05 = 1(1 + i) 6 (1.05) 1/6 = (1 + i) = 1 + i = i So when compounding, a monthly interest rate of % is equivalent to a semi-annual rate of 5% Or a rate of 10% compounded semi-annually is equivalent to a rate of 12( ) = 9.798%

5 (C) Applying Equivalent Rates to Mortgages since mortgages are loans wherein the money is loaned “in the present”, we have to use the present value formula of an annuity ex 1. Determine the monthly payments on a $150,000 mortgage amortized over 25 years if your terms are 6.5% (i) Step 1 is to determine the equivalent monthly interest rate (since by implication, the 6.5% is compounded semi- annually) = (1 + i) 6 i = (1.0325) 1/6 - 1 i = (Or an annual rate of 6.414%) (ii) Step 2 is to simply use the formula to find R 150,000 = R x [(1 - ( ) -300 )/ ] R =

6 (D) Using the TVM Solver on the GC We can analyze the same mortgage using the GDC (1) Hit the APPS key (2) Select 1:Finance (3) Select 1:TVM Solver (4) set N = 300 (why?) (5) set I%= 6.5 (6) set PV = (7) set PMT to 0 (8) set FV = 0 (why?) (9) set P/Y = 12 (why?) (10) set C/Y = 2 (why?) (11) move cursor to PMT (12) hit ALPHA and then the ENTER key (13) you should see the value

7 (E) Examples ex 2. If you have $750 per month to spend on a mortgage payment, what would be the total amount of your mortgage if mortgage rates were 7%. i = (1.035) 1/6 - 1 i = (or 6.9% annually) so now make some assumptions as per the amortization period (let = s say 15, 20, 25 years) PV = 750[(1 - ( ) -180,-240,-300 )/ ] PV = 83, PV = 97, PV = 107,079.26

8 (E) Examples ex 3. If your $125,000 mortgage is amortized over 22 years at 6.75%, how much interest have you paid when you finally have paid off your mortgage? i = ( ) 1/6 - 1 i = Now find R: 125,000 = R x [(1 - ( ) -264 )/ ] R = so if you make 264 monthly payments of $903.06, you pay $238, on the principal of $125,000, meaning you have paid $113, in interest over the 22 years of your mortgage.

9 (F) Internet Links To help you out with the mortgage calculations, many banks have websites with on-line calculators, that will allow you to quickly enter the relevant numbers and immediately calculate mortgage amounts, etc... Some of these "calculators" are found at the following websites: From the Bank of Montreal ==> go to the Calculator option (in the column on the bottom right where is says "Payment Calculator“From the Bank of Montreal ==> go to the Calculator option (in the column on the bottom right where is says "Payment Calculator“ From the Bank of Nova Scotia ==> go to the "Mortgage Payment Calculator", halfway down the column on the right side of the page ==> you will find this calculator gives you some great additional information about your mortgage!!From the Bank of Nova Scotia ==> go to the "Mortgage Payment Calculator", halfway down the column on the right side of the page

10 (F) Homework Nelson Text, p178, Q3,6,8 is work with equivalent rates Nelson Text, p192, Q6-12 is work with mortgages page 170, Q1ace,2ac,4-7,12,19