Let's look at a typical yield farm, where they state an APY (annual percentage yield) as +100% for example. The traditional definition of APY is the real rate of return earned on an investment taking into account the effect of compounding earnings. Using this terminology would indicate that the yield farm was compounding earnings for you. That is simply not the case. A more applicable terminology to use would be APR (annual percentage rate), meaning the annual rate earned through an investment. By definition this would mean that your 100% yield farm would double your original investment at the end of year 1 without reinvesting any earnings. But what about if you reinvested that entire amount the next year and the year after that?
Growth whose rate becomes ever more rapid in proportion to the growing total number or size. The simple formula for this is growth = (1 + r)^x , where 'r' = return and 'x' = number of 'times'. For example, your money doubles every year if you get 100% yearly return. After 3 years you would have 8x your original investment.
growth = (1 + 100%)^3
A typical investment does not just pay out on a yearly basis, but in smaller terms (ie: daily, monthly, etc). For yield farming, returns are even paid out on a per block basis. With an average of 28,800 blocks a day and cheap transaction fees this can allow for a significant amount of exponential growth or compounding of your return. Let's look at how to break that down...
- Compound = P * (1+r/n)^nt Example : 100 * (1+1/12)^(12*1)
- P = principal or starting balance
- r = APR = 100%
- n = compounding periods = 12 months
- t = time = 1 year
- The simple APY calculation in excel can also be stated as =EFFECT(r, n)
Year 1 end would be 261 tokens or 161% APY versus 100% APR w/o compounding