Difference between Apr and Ear

APR, or the Annual Percentage Rate, on a student loan is one of the most important factors that should be considered before a loan is taken out.  More important however is to recognise the subtle (but potentially significant) difference between APR and effective APR, otherwise known as EAR.  Because of the way these are calculated, a student loan (or any other loan for that matter) may have a relatively low APR and have a much higher EAR.

APR is simply the ‘headline’ rate of interest that you must pay on the loan.  If the loan has interest of 5% calculated monthly then the APR for the loan will be 12 x 5% = 60%.

Banks in the UK and US are required to disclose this number before the loan is agreed upon, but they may not mention the EAR, which will, due the way it is calculated, be a higher number than the APR.  It is therefore very much worth taking the time to find out what the EAR is as well as the APR – or, failing that, calculate it yourself.

EAR is the actual rate of interest that you will be paying on the loan, because it is takes account of monthly compounding of interest.  If interest is only calculated annually, then EAR = APR.  However, if interest is calculated monthly, then the amount that must be repaid will increase in month 1, meaning that if you took out a \$100 loan in month 1, in month 2 5% is added and you must now pay interest on \$105 of loan.  This therefore increases the amount you must repay over and above the APR.

The EAR or compound interest can be calculated according to the following formula:

EAR = (1 + r)^n

Where A is the initial amount borrowed, r is the interest rate and n is the number of periods.  Thus for a \$100 loan at 5% monthly rate (60% APR) we calculate an EAR of:

EAR = (1 + 0.05)^12

In this case therefore EAR = 79.5%, which is significantly above the 60% APR.  It is also worth bearing in mind that banks may add an additional administration fee every month which may increase the EAR even further without affecting the APR.

The effect of a 20% higher rate of interest than you expected on a loan as large as a student loan is extremely significant.  Of course, in general such a high rate will not be charged, however the difference between APR and EAR should be noted and these numbers carefully looked up or calculated before a loan is taken out.