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APR, What is it?

A textbook definition of Annual Percentage Rate, APR, is as follows. Charges imposed on a borrower to obtain a mortgage, expressed on an annualized basis as an interest rate. The APR includes the annual interest rate (AIR), loan fees and points. In the USA the APR is meant to disclose the total cost of borrowing. In Canada the APR is defined in section 6 of the Federal Interest Act in an ambiguous manner and is generally understood to mean effective interest rate (EIR). In Canada, Ontario specifically, the total cost of borrowing, TCOB is calculated as the new EIR because of loan fees and points.

Here is an American APR example (taken from a printed booklet) showing why you should be very careful acting upon "rules of thumb". Which is better? Loan#1, a $100,000, 30 year
loan at 10% plus 3 points or Loan#2, a $100,000, 30 year loan at 10.25% plus 1 point. An image of the actual page of the booklet is shown.

The example in the booklet is wrong because this simple
rule of thumb was used. Loan #1 is better for the borrower
using the APR as the yardstick. Loan #1 has an APR of
10.3657% and Loan #2 an APR of 10.3716% which is
greater resulting in more interest being charged.

Before the APR can be appreciated it sometimes helps
to understand other names for the various interest rates
used in the industry. Click Here for an explanation.

In loan #1, the APR is nothing more than the new annual interest rate of 10.3657% because of the $3000 (3 points is 3% of $100,000 = $3000). Changing the Principal to $97,000 and recalculating the annual interest rate gave a new rate of 10.3657%. The borrower is making monthly payments based on $100,000 even though the net amount left is $97,000 thus the rate in reality is 10.3657%. Because of the up front $3000
charge the annual interest rate became 10.3657%.

In loan #2, the APR is nothing more than the new annual interest rate of 10.3716% because of the $1000 (1 points is 1% of $100,000 = $1000). Loan#2 is the more expensive loan (because of the APR method) because the APR is 10.3716% which is greater than 10.3657%. So much for the books
generalized rule of thumb that incorrectly shows that Loan#2 is better. In fact Loan #1 is better by $1,257 in less interest after 6 years (comparing accumulated interests).

When the APR is meaningless!
If the calculation of the mortgage's APR is based upon the 360 day year, aka, the bankers year then the APR is of value. A $100,000 loan at 6% using monthly compounding has an interest cost of $500 the very first month. The interest factor is .005 per month and is CONSTANT each month as the year is assumed to be divided into 12 equal 30 day months or 0.5% per month.

If the loan or mortgage is an exact day monthly payment based upon a 365 day year or an exact day monthly payment based upon a 360 day year, ..the APR is not accurate. The algebraic formulas cannot take into account the changing monthly interest factor. Consider a $300,000 mortgage at 6% for 30 years. Taking into account total fees of $3,000, the lender that uses a 365 day year monthly schedule will collect $1,144 more in interest over the 30 years (comparing spreadsheet interest), yet both lenders would quote you an APR of 6.094%. This screenshot demonstrates the point.




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