APR vs EAR: Understanding the Key Difference

Imagine you’re planning a road trip across the country. You see an advertisement for a car loan with an interest rate of, let’s say, 5 percent. That 5 percent is likely the Annual Percentage Rate, or APR. Think of APR as the advertised sticker price for the cost of borrowing money for a year. It’s a standardized figure designed to help you compare loans from different lenders. It includes not just the interest rate itself, but also other mandatory fees associated with the loan, like origination fees. It’s meant to give you a more complete picture of the total cost of borrowing over a year, presented as a single percentage.

Now, let’s say you are not just taking a road trip, but you are making several shorter trips throughout the year, each time accumulating rewards points on a credit card that also charges interest. The Effective Annual Rate, or EAR, comes into play here. EAR represents the actual interest rate you pay or earn over a year, taking into account the effect of compounding. Compounding is like earning interest on your interest.

To understand compounding, think about planting a seed. If you plant a seed and it grows into a plant that produces more seeds, and then those seeds grow into even more plants, that’s compounding in nature. In finance, it’s similar. With compounding, the interest earned in one period is added to the principal, and then in the next period, you earn interest on the original principal plus the accumulated interest.

APR often assumes simple interest, meaning interest is calculated only on the original principal amount. It doesn’t factor in the effect of interest being added back into the principal and then earning more interest on that larger sum. EAR, on the other hand, explicitly accounts for this compounding effect.

Let’s consider a concrete example. Suppose you deposit $100 into a savings account with a stated APR of 10 percent, compounded annually. In this case, the APR and EAR are the same, 10 percent. After one year, you’ll have earned $10 in interest, and your total balance will be $110.

However, if that same 10 percent APR is compounded monthly, things change. The monthly interest rate is the annual rate divided by 12, which is approximately 0.833 percent. In the first month, you earn 0.833 percent of $100, which is about 83 cents. This interest is added to your principal, so now you have $100.83. In the second month, you earn 0.833 percent on $100.83, which is slightly more than 83 cents. This process continues throughout the year. Because you are earning interest on interest each month, the total interest earned over the year will be more than the simple 10 percent calculated on the initial $100.

In this scenario with monthly compounding at a 10 percent APR, the EAR will be slightly higher than 10 percent. It will be closer to 10.47 percent. This difference, while seemingly small in this example, can become more significant with larger amounts of money or over longer periods. The more frequently interest is compounded – daily, weekly, monthly, quarterly, or semi-annually – the greater the difference between the APR and the EAR.

Therefore, when comparing financial products, especially those involving borrowing or investing, it’s crucial to understand both APR and EAR. APR is useful for initial comparisons, as it provides a standardized rate. However, EAR gives you a more accurate picture of the actual cost of borrowing or the true return on your investment, especially when compounding is involved. Think of APR as the menu price at a restaurant and EAR as the final bill including taxes and service charges – EAR gives you the real total cost. For savers, a higher EAR is generally better, while for borrowers, a lower EAR is preferable. Always look beyond the advertised APR and consider the compounding frequency to truly understand the financial implications.