MAT133Y5 Lecture : 1. Mortgages
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Mortage loans are commonly quoted with a nominal rate compounded semi-annually; but the payments are monthly. To nd the monthly payments in this case one nds the e ective monthly rate of interest. Let r be the nominal rate compounded semi-annually; let i be the e ective monthly rate of interest. To nd i in terms of r we equate the e ective annual rate of compounding semi-annually with the e ective annual rate of compounding monthly. Hence (1 + i)12 1 = (cid:0)1 + r. 2 (cid:1)2 1 (cid:1)2 (cid:1) 1 (cid:1) 1. Take r = 12 , so i = (1. 06) 1. Note that the e ective monthly rate of 0. 98% is less than 1%, which is simply the nominal rate divided by twelve. Find the monthly payments for a 25-year, ,000 mortgage at 12% compounded (a) semi-annually, (b) monthly. The monthly payment for a mortgage is given by.
