Quite often we are asked to calculate payments or we are asked why the payment is different from the one I calculated online? Or have you ever wondered why the cost of borrowing rate is higher than the rate you thought you were locked-in at. Well normally there is a simple answer. In Canada, interest charged on mortgages is determined using a semi-annual interest calculation. Click here for an Excel based Canadian mortgage calculator, or to learn how to do these calculations by hand see below. I will write a two part article this week on how to calculate your mortgage payment by hand. Here is how to calculate the effective interest rate:-
The first thing to realize is that there are three types of interest calculations:- simple interest, compound interest and effective interest.
Simple Interest – The cost of borrowing money, calculated by applying the interest rate to the original principal amount only. In contrast to compound interest, interest is not charged on interest.
(Simple Interest = P x i x n)
Compound Interest – Interest charged not only on the principal sum but also on interest amounts charged, but not paid, in preceding periods that accumulate as new principal.
Effective Interest – The actual rate that the borrower must pay on a loan after the effects of compounding are considered. It is also known as the true rate. It differs from the nominal interest rate.
(Efffective Interst = (1+(i/m)m- 1)
Mortgage interest is always compounded semi-annually in Canada. In the US this is not the case, mortgage interest is compounded annually.
To Calculate Mortgage Payments and Interest Rates you will need the following information:
1. Nominal or Annual Interest Rate (I)
2. Compounding Periods per Year
3. Effective Annual Rate
4. Mortgage Amount (Present Value)
5. Future Value of the Mortgage
6. Total Number of Compounding Periods (# of years x # of periods per year)
7. Payment per compounding period
Calculating the Effective Interest Rate
Annual Interest Rate = 7%
Mortgage Amount = $150,000
Since mortgage interest is calculated on a semi-annual basis there are 2 compounding periods:
1. Calculate the Semi-Annual Interest Rate
Semi-Annual Interest Rate = Annual Interest Rate/2
Semi-Annual Interest Rate = 3.5% (7%/2)
2. Calculate the Interest for the First Period
Interest = Mortgage Amount * Semi-Annual Rate
Interest = $150,000*3.5%
Interest = $5,250
Add interest to the original total mortgage amount
$150,000+$5,250=$155,250 (New Mortgage Amount)
3. Calculate the Interest for the Second Period
Interest=New Mortgage Amount*Semi-Annual Rate
Interest=$155,250*3.5%
Interest=$5,433.75
4. Calculate the Total Interest
Add interest from the first period to the second period
Total Interest = $5,250+$5,433.75
Total Interest = $10,683.75
5. Calculate the Effective Interest Rate
Effective Interest Rate = Total Interest/Original Mortgage Amount
Effective Interest Rate = $10,683.75/$150,000
Effective Interest Rate = 7.12%
Stayed tuned for how to calculate your Mortgage Payment and future blogs on determining mortgage affordability.
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