# Essay on EAR And APR And Why It Matters

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EAR and APR and why it matters. Summarized by Karen Chiykowski

APR annual percentage rate; a definition, APR = rate/period x # periods per year = periodic rate x # periods per year. (No compounding) Used by lenders to describe loans and used by financial institutions to describe some types of savings.

EAR effective annual rate; EAR includes compounding and allows user to compare different periodic cash flows on an annual return basis. Calculation of EAR is required to compare investments with different cash flows or loans with different APRs, periods or cash flows.

Periodic rate= rate per period.

Calculating EAR based on APR or periodic rate

(1+ EAR) = (1 + APR/# periods per year)# periods per year = (1 +periodic rate)# periods per year
This is exactly the same as:
EAR = (1 + APR/# periods per year)# periods per year - 1 = (1 +periodic rate)# periods per year - 1

Calculating periodic rate based on EAR

(1 + EAR)1/# periods = (1 +periodic rate) = (1 + APR/# periods per year)
This is exactly the same as: periodic rate = APR/# periods per year = (1 + EAR)1/# periods -1

1. Use APR to determine the loan payment.
Loan APR rates are the basis from which the loan payment is calculated. Most loans are required to be advertised with an APR and the number of payment periods per year. For example car loans may be advertised as 2.9% APR with monthly payments. This way the borrower can determine their monthly payment based on any borrowed amount.

Eg periodic rate is monthly, 6%/12 months = .5% per month.
Using your calculator, a 48 month loan of \$30,000 would require a \$704.55 monthly payment.

2. Use EAR to determine which loan (or in other circumstances which investment) is the better deal.

You might have to compare the above car loan to using a line of credit. If the line of credit is 5.8 % APR based on daily compounding you would have to determine which was the lower rate for your \$30,000 loan.

The only way to compare the two loans is to convert to EAR. Remember, EAR includes compounding and takes into account the different compounding rates and compounding periods. It is not always obvious by just looking at the APR and compounding periods. You usually have to calculate the EAR to make the comparison.

EAR of car loan: EAR = (1 + APR/# periods per year)# periods per year - 1
= (1+.06/12)12 -1 = (1+.005)12 -1 = 1.0617 -1 = 0.0617 = 6.17%.

EAR of line of credit: EAR = (1 + APR/# periods per year)# periods per year - 1
= (1+.058/365)365 -1 = (1+.0001589)365 -1 = (1.0597) -1 = .0597 = 5.97%.

We have converted both loans to EAR which include compounding.
The line of credit has a lower effective rate.
All other factors being equal, use the line of credit to buy the car.

3. Use EAR to determine which savings account to use:

Compare a 5 year 10% APR GIC with semi annual compounding to a 5 year GIC with a stepped interest rate of 8% the first year, 8.5 % the second year, 9 % the third year 10% the 4th year and 12% the final year. Demonstate which GIC will provide the highest return?

First GIC. EAR = (1 + periodic rate)# periods – 1 = (1 + .10/2)2 – 1 = (1.05)2 -1 = 1.1025 – 1 = 0.1025 = 10.25%
Second GIC EAR = [(1.08)(1.085)(1.09)(1.10)(1.10)]1/5 -1 = 1.091 – 1 = 0.091 = 9.1%

4 . Convert from EAR to APR if you are given information annually but your cash flows are not annual.

Assume you are forecasting retirement requirements. Based on decades of information about increasing and decreasing annual stock and bond market returns you expect annual returns to be 8% per year on average for your retirement savings portfolio. However you wish to invest twice monthly not annually. Let’s say that you want to invest \$24,000 per year but expect to invest \$1,000 semi monthly (twice per month). The problem is that the return information is annual. The annual return information includes compounding (remember, these returns are based on…