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APR vs APY

Often associated with staking and farming are the two types of returns an investor can expect, APR (annual percentage rate) and APY (annual percentage yield). Knowing the difference between these 2 is very important.

(concepts here are going to be fairly basic for educational purposes.)

Annual percentage rate, would be the percentage of return you will earn over a year.

At 12% APR, if you invest 1000 dollars, after a year you will have earned an additional 120 dollars, for a total of $1120.

Annual percentage yield is a bit more complicated. APY takes into account compound interest earned throughout the year. This could be a bit like a savings account at your bank.

The equation may look a bit daunting, but is really simple once explained.

$A=P(1+ \frac{r}{n})^{nt}$

A = Final amount

P = Principal (initial deposit)

r = interest rate

n = number of compound periods per unit of ‘t’

t = time

As an example, we can use $1000 as the principal (P) at a 12% interest rate (r), for a year (t), that compounds monthly (n).

$A =1000(1+\frac{.12}{12})^{12}$

This is how we would input all the proper variables, and using the order of operations, we would take the following steps to get to our final amount (A)

$A=1000(1+.01)^{12 }$

First step would be to reduce the fraction within the parenthesis. (for sake of this tutorial, I will also add the total quantity within the parenthesis, to get 1.01) Also the exponent gets resolved here, 12 * 1 is 12.

$A= 1000(1.12682503013)$

Following the order of operations (PEMDAS), we next would resolve the exponent part of the equation. 1.01 raised to the 12th power is 1.12682503013

$A= 1126.83$

The last step is simple multiplication and gives you the final total for 1 year worth of investing at a 12% APY.

If you deposited the same $1,000 into the bank at a 12% APY as opposed to 12% APR, your final total would be 1126.83. There isn't a huge difference, but after 5 years it becomes 1600 (APR) to 1816.17 (APY). Every time your account compounds, any interest earned is added to your total, and the next compounding period earns interest on the new total. A common compounding period is 1 month.

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