What is APR and APY

You don't know what is APR or APY or the difference between the two? Then, you might not be earning as much as you could 😉 . Read this article and become a more profitable investor.

Memento (read below first)

Amount $I_n$ after $n$ days with an initial amount $I_0$ and no compounding:

I_n = I_0 \left(1 + n \frac{\text{APR}}{365}\right)

Amount $I_n$ after $n$ days with an initial amount $I_0$ and daily compounding:

I_n = I_0 \left(1 + \frac{\text{APR}}{365}\right)^n

Relationship between APY and APR:

\text{APY} = \left(1 + \frac{\text{APR}}{365}\right)^{365} - 1

APR

Let's say you bought some CAKE. You can buy CAKE on LP-Swap.

If your CAKE sit in your wallet, then you are not earning as much as you could! PancakeSwap has numerous Syrup Pools where you can deposit CAKE and earn tokens.

For example, if you deposit your CAKE in the CAKE pool, you will earn CAKE:

Here, I deposited ("staked") 10 CAKE (≈ $380.10 at screenshot time), waited several days and have now earned 1 CAKE (≈ $38.01).

The APR gives you how much CAKE you will earn if you stake 1 CAKE for 1 year in the pool. Here, ${\text{APR} = 90.97\%}$ . So if I stake 10 CAKE for 1 year, I will earn a reward of:

10 \times 90.97\% = 9.097 \text{ CAKE}

The APR of the CAKE pool might change over time because the amount of CAKE staked might vary over time while the amount of CAKE rewards for the whole pool is constant. So the more CAKE staked, the less CAKE rewards per CAKE staked.

You don't have to wait 1 year to start collecting rewards. In fact, you can collect rewards every second (but it would be expansive in transaction fees)! In my case, if I collect rewards in 1 day, I will earn a reward of:

10 \times \frac{90.97\%}{365} = 0.0249 \text{ CAKE}

More generally, if you stake $I_0\text{ CAKE}$ , then after $n$ days, you will earn a reward of:

I_0 \times \frac{\text{APR}}{365} \times n \;\; \text{CAKE}

assuming APR stays constant.

APY

When you stake CAKE in the CAKE Syrup Pool, there is a magic way to drastically increase the amount of CAKE you earn: it is called compounding and consists in collecting rewards and staking them again.

The important thing to understand is that your CAKE rewards are proportional to your CAKE staked. So by compounding (i.e. collecting rewards and staking them again), you increase your amount of CAKE staked and therefore increase the amount of CAKE rewards you will earn.

Let's say I stake $10\text{ CAKE}$ at an APR of 90.97%. During the first day, I will earn:

10 \times \frac{90.97\%}{365} = 0.249 \text{ CAKE}

I then compound (i.e. collect my rewards and stake them again). I now stake ${10 + 0.249 = 10.249\text{ CAKE}}$ . During the second day, I will now earn:

10.249 \times \frac{90.97\%}{365} = 0.255 \text{ CAKE}

whereas I would only have earned $0.249\text{ CAKE}$ if I had not compounded.

More generally, if I stake $I_0\text{ CAKE}$ , wait 1 day and compound, then my stake will be:

I_0 + I_0 \times \frac{\text{APR}}{365} = I_0 \left(1 + \frac{\text{APR}}{365}\right)

If I wait another day and compound, my stake will be:

I_0 \left(1+\frac{\text{APR}}{365}\right)^2

After $n$ days of compounds, my stake will be:

I_0 \left(1 + \frac{\text{APR}}{365}\right)^n

If I substract the initial stake $I_0$ , I get the amount of rewards earned after $n$ days:

I_0 \left(\left(1 + \frac{\text{APR}}{365}\right)^n - 1\right)

The APY gives you the amount of rewards you will earn per year if you compound. Assuming you compound daily, this is the formula to calculate the APY from the APR:

\text{APY} = \left(1+\frac{\text{APR}}{365}\right)^{365} - 1

From this formula, it is not obvious that APY might be much bigger than APR, so let's calculate the APY for the CAKE pool. With $\text{APR} = 90.97\%$ , we get:

\text{APY} = \left(1+\frac{90.97\%}{365}\right)^{365} - 1 = 148.07\%

If you initially staked $1000 worth of CAKE and compounded rewards everyday for 1 year, you would have earned $1480 worth of CAKE rewards, instead of $909 if you had not compounded. This is a big increase!!

But you might be thinking: "Well, compounding everyday is exhausting...". You are lucky because PancakeSwap has a pool, called "Auto CAKE", that does the compounding for you!

Deposit your CAKE in this pool and it will do the rest: it will stake your CAKE in the "Manual CAKE" pool and do the compounding multiple times per day for you.

Lastly, you might wonder why the APY displayed is 143.84% whereas we calculated 148.07%? It is because PancakeSwap takes 2% of your rewards at each compound.

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