APR, EAR and Period Rates - Explained PDF

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APR, EAR, and Period Rates...

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APR, EAR and Period Rates

Rule 1: If Compounding occurs annually (once a year) e.g. TD Bank pays you 8% compounded annually on your deposit, then EAR =APR and there is no period rate. Rule 2: However, if compounding occurs more frequently (e.g. monthly), then EAR >APR and the APR reported is a “fake” rate. Example: Your credit card charges you an interest rate of 1.5% per month (“period rate”). 

Your statement would show an 18% annual rate, computed as 1.5% x 12.

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Yet, if you owed $100 on this account, and did not make any payments for an entire year, the balance at the end of the year would be $119.56 rather than $118. That higher balance implies 19.56% interest instead of 18%. It is higher because of monthly compounding, and is computed as $100 x (1 + .015)12.

To distinguish between these rates, we call 18% the APR, and 19.56% the EAR. So now we have three different interest rates for the credit card:  the 1.5% monthly rate (im),  the 18% APR, and  the 19.56% EAR. APR is a stated nominal rate that does not reflect reality and is lower than EAR if compounding occurs more than once a year (that’s why financing firms such as car dealerships quote you APR and not EAR.) EAR more accurately reflects the true financing rate. Rule 3: Relationship between EAR and APR If im is the period rate and m is the number of periods per year. 

APR = im x m  APR is similar to simple interest calculations

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EAR = (1 + im)m - 1  EAR is similar to compound interest calculations

Note: the common link between EAR and APR is im (im is the same variable for both equations). So if you can convert between EAR and APR as long as you know im and m.

General Problem Solving (IMPORTANT) 1. You only calculate APR if you are asked to solve for APR in a question, which is not very often. (e.g. Usually APR's are stated in the question and you have to find the period rate (im) or EAR from it. (the point being that finance companies and banks try to "trick" you with posted rates that are APRs.)

2. Match the interest rate input for your calculator to the payment frequency. For example, if you have monthly payments, I for your calculator must be a monthly rate (im) 3. If a rate is quoted in a problem and the word “effective” is not explicitly stated, assume the rate is an APR. Mortgage Problems To further complicate matters, in Canada the posted mortgage rate is a “quasi” APR. It is quoted as an APR but compounded semi-annually. To find im for mortgage problems only, you cannot divide the stated APR rate by 12 (as per the above equation). Instead you must first convert the posted rate to an EAR and then find im. The more problems you attempt from the back of Chapter 5 and from the Extra Files folder, the more you will understand the difference between APR and EAR....