APR vs EAR: How Does Compounding Frequency Impact Returns?

Imagine you’re planting a seed and expecting it to grow into a money tree. The Annual Percentage Rate, or APR, is like the advertised growth rate for your tree, let’s say ten percent per year. It sounds straightforward, right? Ten percent growth on your investment each year. However, the reality of how your money grows is often a bit more nuanced, and this is where the concept of Effective Annual Rate, or EAR, comes into play.

Think of compounding frequency as how often you water your money tree. If you only water it once a year, the growth is pretty much exactly as advertised, the ten percent APR. This annual watering, or annual compounding, means the interest is calculated and added to your principal only once a year. So, if you start with one hundred dollars, after one year, you’ll have one hundred and ten dollars. In this case, the EAR is the same as the APR, ten percent.

But what if you water your money tree more often? Let’s say you water it twice a year, or semi-annually. This means interest is calculated and added to your principal every six months. With our ten percent APR, for semi-annual compounding, the interest rate for each six-month period is actually half of the annual rate, which is five percent.

So, after the first six months, your initial one hundred dollars grows by five percent, becoming one hundred and five dollars. Now, for the second six months, the interest is calculated not just on the original one hundred dollars, but on the new balance of one hundred and five dollars. Five percent of one hundred and five dollars is five dollars and twenty-five cents. Adding this to the one hundred and five dollars, you end up with one hundred ten dollars and twenty-five cents at the end of the year.

Notice something interesting? Even though the APR was still ten percent, you actually earned more than ten percent overall. Your effective annual rate, the actual growth you experienced, is now ten and a quarter percent, slightly higher than the advertised APR.

This difference arises because of the magic of compounding. When interest is compounded more frequently, you start earning interest on the interest you’ve already earned, sooner. It’s like your money tree starts producing fruit, and then the fruit itself starts growing more fruit.

Let’s take this even further. Imagine watering your money tree every month, which is monthly compounding. Now, the ten percent APR is divided into twelve monthly periods, meaning the interest rate per month is roughly 0.83 percent. You earn a little bit of interest each month, and each time, that earned interest gets added to your principal, becoming part of the base for calculating the next month’s interest. If you calculate this out, you’ll find that the EAR becomes even higher than ten and a quarter percent.

As you increase the compounding frequency, from annual to semi-annual to quarterly, then to monthly, weekly, daily, and even continuously, the EAR will continue to increase, although at a decreasing rate. It will always be higher than the APR, except in the case of annual compounding where they are the same.

Think of it like this: the APR is the advertised speed limit for your money’s growth, but the EAR is the actual speed you achieve, factoring in how frequently you are accelerating. The more frequently interest compounds, the more often your money gets a little boost, leading to a slightly higher overall growth rate over the year.

Understanding the difference between APR and EAR is really important when comparing financial products. For loans, a higher EAR means you’re actually paying more interest over the year, even if the APR seems comparable. For investments, a higher EAR means your money is growing faster. Always look beyond just the APR and consider the compounding frequency to truly understand the effective annual rate, the real growth or cost of your money.