Mortgages & Equivalent Interest

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Jonas Wells
5 years ago
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1 Mortgages & Equivalent Interest A mortgage is a loan which you then pay back with equal payments at regular intervals. Thus a mortgage is an annuity! A down payment is a one time payment you make so that the amount you borrow is less. An annual interest rate is often referred to as a nominal rate. In Canada, a standard mortgage compounds its interest semi annually and the payments are made monthly. This discrepancy between compounding period and payment frequency means you must calculate the equivalent interest rate. Jun 7 8:05 PM Consider a mortgage with 12%/a interest. It is compounded semi annually, but applied to monthly payments. In order to determine the future value of this mortgage, you would first have to determine the equivalent interest rate. 1. Determine the equivalent yearly rate based on semi annual compounding. 2. Convert (1+ i) 2 for the first equivalent rate to (1+ i) 12 if the rate was compounded monthly. Jun 7 8:20 PM 1

Notes on equivalent interest In general, equivalent interest can be calculated as follows: 1.

Convert the equivalent annual rate to the required compounding period: e.g., 10.

For example, present value PV Problem : How much should I invest now (PV) to provide regular payments (R) over some time period,

2 Notes on equivalent interest In general, equivalent interest can be calculated as follows: 1. Convert given interest to an equivalent annual rate: e.g., 10%/annum, compound semi annually so the equivalent annual rate is 10.25% 2. Convert the equivalent annual rate to the required compounding period: e.g., 10.25%/a to equivalent monthly Jun 11 5:13 PM A mortgage problem is similar to a annuity problem. For example, present value PV Problem : How much should I invest now (PV) to provide regular payments (R) over some time period, assuming I can make some interest on my investment (i). Mortgage Problem : The bank has invested some amount for me (by buying me a house) now (PV), but they expect me to pay back this loan with regular payments (R) over some time period (with interest, i). or Jun 9 10:08 PM 2

3 Ex.1 A house is purchased for $ with a $ down payment. A 5%/a mortgage, compounded semiannually, is taken out for 25 years. a) Determine the monthly interest rate. b) Calculate the amount that needs to be borrowed for the mortgage. c) Determine the monthly payments that are to be made. Jun 7 8:21 PM Ex.1 (continued) A house is purchased for $ with a $ down payment. A 5%/a mortgage, compounded semi annually, is taken out for 25 years. c) Determine the monthly payments that are to be made. Jun 7 8:17 PM 3

4 Ex.1 (continued) A house is purchased for $ with a $ down payment. A 5%/a mortgage, compounded semi annually, is taken out for 25 years. d) What is the total cost of the mortgage, as compared to the amount borrowed from the bank? e) Determine the total interest paid on the mortgage. Jun 8 12:09 PM Amortization tables are data organized in a way that lets you view the various values of a mortgage over its lifetime. For each payment, it will generally show you (a) how much goes to the principal (b) how much goes to interest (c) the remaining balance on the principal bin/amortize Jun 9 10:37 PM 4

5 Assigned Work: p.541 # 9 p.567 # 8, 13 Consider a mortgage of $ amortized over 25 years. The bank offers a 5.25% interest rate compounded semi annually for a 10 year term. a) Calculate the equivalent interest rate. b) Determine the monthly payment. c) Determine the total amount paid in 10 years. d) Determine the total interest paid in 10 years. Jun 8 8:02 AM 5

REVIEW OF KEY CONCEPTS

REVIEW OF KEY CONCEPTS 7.2 Compound Interest Refer to the Key Concepts on page 507. 1. Find the amount of each investment. a) $400 at 6% per annum, compounded monthly, for 5 years b) $1500 at 4.25% per