Simple interest and compound interest

Since APY calculations use compound interest, let’s start by reviewing simple and compound interest. Simple interest is a set rate entirely based on the original investment. Any money earned from interest is not included in future interest calculations. Compound interest is interest on both the original investment plus the money from previously earned interest. Compound interest grows your investment at a faster rate than simple interest.

Here is a formula for simple interest earned:

Simple interest earned = P × I × T

P = Principal

I = Interest rate (annual)

T = Time period held

For example, let’s imagine you put $10,000 of a stablecoin like USDC in a crypto protocol that offers a five percent annual interest rate, and held it for four years. The amount of interest earned is:

$2000 = $10,000 × 0.05 × 4

When you withdraw all of your money after four years you will have $12,000.

Next, let’s look at compound interest. As you would expect, calculating compound interest is more complicated than simple interest.

Compound interest earned = [P × (1 + I)n ] – P

P = Principal

I = Interest rate (annual)

n = Number of compounding periods

As before, let’s imagine you put $10,000 of USDC in a crypto protocol that offers a 5% annual interest rate, and held it for four years. This crypto protocol compounds once a year. If you hold it for four years then the number of compounding periods is four:

$2155.06 = [$10,000 × (1 + 0.05)4 ] – $10,000

Because compound interest includes money accumulated in previous periods, it grows at an ever accelerating rate.

When deciding between different investment products, it’s important to know the interest rate and the compounding periods. For example, an investment of $10,000 at five percent annual percent rate held for four years and compounded:

1 time per year: $2,155.06

4 times per year: $2,198.90

12 times per year: $2,208.95

What is APY?

The annual percentage yield (APY) is a standardized way to calculate the real rate of return on investments for one year. APY is considered the real rate of return earned on an investment because it takes into account compound interest. Compound interest is added periodically to the total investment, increasing the account balance, which makes the subsequent money earned from interest larger. The formula for APY is:

APY= (1 + r/n )n – 1

r = period rate

n = number of compounding periods

It is considered the real rate of return because simply stating the interest rate over one year does not account for discrepancies in the compounding period.

What is the difference between APY and APR?

The key difference between annual percentage yield (APY) and annual percentage rate (APR) is that APY takes into account compounding interest, but APR does not. Additionally, APR includes any fees or additional costs associated with the investment transaction. Put another way, APR is calculated using simple interest and includes fees.

In practical terms there is one important distinction that determines how APY and APR are used. Because APY includes compounding, the calculation will always produce a higher interest rate (a bigger number). Therefore, it is usually preferred when financial products refer to something that will earn people money, such as interest earned on a bank savings account. Conversely, since APR will be a lower interest rate, it is used for things that will cost people money, like the interest rate on a credit card or mortgage.

You can convert from APR to APY to get the real rate. For example, a credit card might advertise an interest rate of 1.5% per month, or an APR of 18%. However if your credit card balance remains for one year, your APY (real rate) will be 19.56% due to the compounding interest added to your balance each month.