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Annual Percentage Rate (APR) for a Loan

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Financial Planning -> Save Money -> Know the interest rate

Annual Percentage Rate on Loans

Make sure you know the interest rate before committing to a loan

In some provinces, lenders are required under provincial consumer protection laws to disclose both the total cost of credit and the annual percentage rate (APR).  The total cost of credit includes additional finance charges such as application, administration and service charges.

In BC, the calculation method for the APR is defined in the Business Practices and Consumer Protection Act Disclosure of the Cost of Consumer Credit Regulation.

In Ontario, the calculation method is defined in the Consumer Protection Act, 2002, Ontario Regulation 17/05, s. 55.

APR using average principal outstanding calculated from amortization table

The APR (for credit agreements other than leases) is defined in both the BC and Ontario regulations, when all interest calculation periods under the credit agreement are of equal lengths, as:

[C ÷ (T × A)] × 100 

where

C is the total cost of credit
T is the length of the credit term, in years, and
A is the average of the principal balances outstanding at the end of each interest calculation period, before any amount is applied against the principal.

If you have an amortization table of your loan, you can use it to calculate the average principal amount outstanding exactly, instead of using our method for estimating the average.  To calculate the average principal, calculate the sum of:

        - for each calculation period in the term of the loan, the outstanding principal amount before any payment is applied.

Then, divide this sum by the number of calculation periods in the term of the loan.

Example using a recent purchase of a 5 year old vehicle from a used car dealership in BC (numbers are approximate):

Vehicle price $11,000
2 year extended warranty 2,500
Subtotal 13,500
GST + PST 1,620
Finance fee 500
Total $15,620
Less down payment * (1,075)
Total loan amount $14,545
 
Monthly loan payment $449.20
Term of loan in years 4.5
Term of loan in months 54

*We are told that there was actually no down payment, although the sales document showed one.  Apparently this was "paid by the dealership", in other words, the price was reduced.  However, there was no corresponding reduction in sales taxes.

The interest rate was not stated on the sale document, so it was calculated using the factors of loan amount, term and payment amount, and an amortization table was produced.  This allowed calculation of the total interest cost (which was stated on the sale document).  The total interest cost and the finance fee are added together to get the total cost of credit.  Here is what we determined:

Total payments ($449.20 x 54) $24,257
 
Total interest costs $9,712
Add finance fee 500
Total cost of credit $10,212
 
Average outstanding principal balance $8,559
 
Annual Percentage Rate (APR)
 = $10,201 / ($8,559 x 4.5 yrs)
26.5%

APR using estimated average principal outstanding

It is fairly easy to do an estimate of the APR that you are being charged.  You need to know

  1. The amount of the loan, excluding additional finance charges such as application, administration and service charges.
  2. The term of the loan in months or years.
  3. The total that will be paid over the term of the loan (# of payments x payment amount)

It's important to realize that over the term of any loan which is repaid with equal payments paid at regular intervals, the average principal amount outstanding on the loan is approximately (actually slightly more than) half of the loan amount.  To estimate the average, add together the beginning loan amount and the payment amount, and divide by two.

bulletaverage loan amount is $7,497, or half of ($14,545 + 449.20).

This results in an estimated APR of 30.3% ($10,212 divided by $7,497 x 4.5), which is significantly higher than the actual APR.

As you can see, the resulting interest rate is lower when using the exact method of calculating the average outstanding principal.  The difference between the two methods becomes greater as the term of the loan becomes longer and the interest rate becomes higher.

See also:

Buying a Vehicle

Tax tip:  Make sure you know the APR you are being charged, and explore other financing options.

Revised: October 11, 2017

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