Here at Cake, there are two terms used for rewards: APY & APR
APY (Annual percentage Yield)
The APY is the annual compounded annuity. This means that the displayed rate in APY is including the compound interest (interest on interests). In order to fulfill the displayed APY rate, the earned interests need to be reinvested in order to earn rewards on those as well. For example if you are using our Staking service, you are given the option to turn Auto-compound on. This will reinvest your earned interests back into the staking pool, and therefore be able to fulfill the given APY rate.
APR (Annual Percentage Rate)
The APR is the Annual return without compound interest. This means that the displayed rate in APR is the return you would get on your base investment in interests. Consequently, if you would be reinvesting your earned interest, that would give you a higher return rate (in APY).
How to Calculate the Annual Percentage Rate?
In order to calculate the total final amount based on APR, follow these steps:
A = [P x (1 + RxT)] where
A = total amount
P = principal (initial investment)
R = interest rate
T = time in years
In the example above, it would be calculated as follows:
A = [P x (1 + RxT)] where
P = 0.5 BTC
R = 7% or 0.07
T = 1 year
A = [0.5 x (1 + 0.07x1)]
A = 0.535
If the investment is retained for a shorter period, the calculation changes. If you hold for three months, you will have held for a quarter of a year (0.25), so you will need to calculate:
A = [P x (1 + RxT)] where
P = 0.5 BTC
R = 7% or 0.07
T = 0.25 years
A = [0.5 x (1 + 0.07x0.25)]
A = 0.50875
That means that you will earn 0.00875 Bitcoin on top of the initial investment if you hold for three months.
How to Calculate the Annual Percentage Yield?
The APY calculation is a bit more complicated than the APR since interest is added to the principal, and then interest is calculated based on the number of periods the amount has been adjusted. The compound interest can be set on a daily, weekly, monthly, annual or perpetual basis.
APY = (1 + r / n)^n - 1 where
r = period rate
n = number of compounding periods
Suppose an investment of 1,000 DFI is made at a compound interest rate of 20% and daily compounding. As a result of the calculation above, an initial investment of 1,000 DFI yields 221 DFI over one year, making a total of 1,221 DFI in the first year and 1,492 the following year. Additionally, higher interest rates and longer holding periods increase earnings.