APR and APY

APR (Annual Percentage Return) is the rate a lender earns on their money or a borrower pays for using another’s money respectively for one year. APY (Annual Percentage Yield) meanwhile is the interest earned or paid on an annual basis.. It could be compounded daily, weekly, monthly etc.

APR usually accounts for simple interest and fees while APY accounts for compound interest alone. To understand this better, one should differentiate simple and compound interests respectively. Simple interest is a fixed percentage of the principal sum while compound interest earns interest on both the original principal and every subsequent interest. In practice, $10,000 invested at 5% Simple interest p.a. for five years becomes $12,500. However, if this same amount was invested with interest compounding yearly, it would have amounted to $12,840. This difference increases as the invested amount, duration and frequency of compounding increases. Financial institutions usually quote APR on some products and APY on some others for marketing reasons. APR values are usually lower than the value of APYs. APRs encourage you to take on debt.

APR and APY in Cryptocurrency

Cryptocurrency has financial products ranging from savings, staking, liquidity mining, yield farming etc. All of these products have quoted APRs or APYs. However, care must be taken when considering taking cryptocurrency interest bearing or paying products offered by different exchanges and platforms. The reason includes:

• Your deposited token can become less in dollar value due to volatility, the dollar value of the interest earned may not recover it.
• You should also note if the interest is a fixed rate or flexible.
• For decentralized protocols, the gas fees as well as any other fees such as reflection must be considered.
• There is also the risk of losing your tokens if the entity goes bankrupt.

How to calculate APR and APY

APR

Key variables:

• Interest paid(I): total amount paid over loan lifetime less principal.
• Fees(f): fees paid apart from interest.
• Principal (P): amount borrowed.
• Duration(T) in years
• Rate(R): the interest rate.

From the formula for calculating simple interest I=PRT100 where I = interest paid, P = principal, R = interest rate or APR and T = time in Year. It can be written as R=IP*T X 100. To compute APR:

1. Replace Interest(I) in above formula with I + f which gives R=I+fP*T X 100.
2. Calculate interest paid as explained in key variables
3. Substitute into the equation in i above and finalize.

APY

Key variables:

• Interest rate(i): which can be computed as total amount paid over loan lifetime less principal
• Duration(t) in years
• Number of compounding per annum(n) which is 365 for daily, 12 for monthly etc. 

From the formula for calculating compound interest A=P(1+in)^nt where A = amount paid, i = interest rate, P = principal, n = number of compounding p.a. and t = time in Year. Interest rate which equals APY can be computed as APY=(1+in)^nt To compute APY:

Simply substitute the values appropriately in the equations and finalize.