Interest rate alphabet soup: APY, APR, Coupon, Yields, SAIR, EAR

Are you confused about interest rates? Why don't all interest rates behave the same way? Let's deconstruct what each type of interest rate means and its effect on your venture.

Often times you’re presented with a variety of interest rates. Whether you’re purchasing a car or investing in a security, it’s easy to not understand what rate actually matters to you (and your investment). Take a look at the security below.

In order to understand what interest rate you are actually facing, we need to understand the two types of interest rates: compounding and non-compounding.

Non-compounding interest rates

These are the interest rates that occur each period and are also known as

• coupon rate

• annual percentage return or APR

• the stated annual interest rate or SAIR

• yield to maturity or YTM

• internal rate of return or IRR

These interest rates do not reflect compounding. Non-compounding interest rates are code - they really can’t be used to

1. determine how much money you’re actually going to earn, or

2. compare other interest rates that you might want to take advantage of.

For both requirements, you need the compounded interest rate.

Compounding interest rate

The compounding interest rate is often referred to as

• annual percentage yield, or APY, or

• effective annual rate, or EAR

It is this interest rate that tells you how much money you’ll have earned on both your principal investment ($100 at t = 0 in our example) and all the interest that you have earned on the principal (t = 1) and previously earned interest (interest on the interest).

In our case, the APY (compounding interest rate) is give: 5.335%. Often, you won’t be given this rate, and you’ll have to calculate it.

Let’s do that.

Calculating the compounding rate

First, we need the non-compounding (coupon or APR) rate. In our example, that is 5.3%.

Next we need to know the number of compounding periods in one year. If you look at our example, you’ll see that the security pays a coupon at the time of maturity, and that maturity time happens in 9 months.

• Coupon rate = 5.3%

• Coupon payment = at maturity

• Maturity = at 9 months

Since maturity happens at 9 months, and there are 12 months in a year, the number of compounding periods is 1.333 (12 divided by 9).

• Compounding periods = 1.333

Now that we have all the necessary information, we can begin our transformation of the non-compounding rate (coupon payment = 5.3%) to the compounding rate.

Convert the non-compounding rate into a monthly rate

In order to start the conversion, we need to divide the non-compounding rate (the coupon rate of 5.3%) with the number of compounding periods in 1 year (1.333).

• effective rate at 9 months = 5.3%/1.33 = 3.975%

The effective rate at 9 months

The effective rate you just calculated is 3.975%. With one more modification, you will come up with the effective annual rate (EAR). This EAR will allow you to

• quantify how much money you will earn on your investment, and

• compare this investment with other investment opportunities.

To calculate the effective annual rate, we need to revisit 1.33 - 1.33 is the number of compounding periods in one year.

Let’s say we invest $1 into this opportunity. And we let our investment compound over 1.33 periods. We are then left with

$1*(1+3.975%)^1.33 periods = $1.05335

Subtract your original $1 investment and you’ll get the amount of interest you earned

$1.05335 - $1 = $0.5335 → 5.335%

The next time you make an investment (car, security, bank instrument), you’ll have a better understanding of the interest rates quoted and how to calculate the effective annual rate (if it is not given to you) so you can make informed and accurate choices.