Basic general formula to find compound interest can be derived as follows.
Future value = Principal value * (1 + rate of interest) time Period,
Mathematically, F = P * (1 + R) x, C.I. = F – P.
Where 'F' indicates future value, 'x' is time period, 'P' denotes the principal value, 'R' is the interest rate or periodic rate which is always fixed and is decided on annual scheme.
Now it is easy to calculate daily compound interest using above formula. Change will only be in interest rate to achieve the target.
Lets derive the formula to understand how to calculate daily compound interest.
For this we have to divide interest rate (R) by 365 since there are 365 days in a year. Interest rate is fixed annually.
Mathematically, F = P * (1 + R / 365) x,
Assume that amount borrowed is $ 20000 and if interest rate is 8% then after one year interest that has to be paid, is $ 1600. Thus at the end of year amount which is to be paid is $ 21600.
To calculate daily compound interest, divide the interest rate by 365. In this case the 8% (which can be written in Decimals as 0.08) will be divided by 365 (0.08/365) which is equals to 0.00022. Since principal amount is $ 20000, multiply it by 0.00022 which is equals to 4.4, hence daily compound interest will be $ 4.4.