Just like the title I'm looking for the formula to convert APR to monthly when I also know compounding frequency
eg APR is 8% and being compounded daily what is the monthly interest rate I earn.
Or the same where it is compounded every six months.
Probably simplest to convert to effective annual rate first:
So, calculating 8% compounded daily as monthly rate,
i = 0.08 n = 365 r = (1 + i/n)^n - 1 = 0.0832776 = 8.32776 % effective annual interest m = ((r + 1)^(1/12)) - 1 = 0.0066882 = 0.66882 % monthly interest equivalent to APR compounded monthly = 12 * m = 8.02584 %
and calculating 8% compounded six-monthly as a monthly rate,
i = 0.08 n = 2 r = (1 + i/n)^n - 1 = 0.0816 = 8.16 % effective annual interest m = ((r + 1)^(1/12)) - 1 = 0.0065582 = 0.65582 % monthly interest equivalent to APR compounded monthly = 12 * m = 7.86984 %
In one step:
m = ((1 + i/n)^n)^(1/12) - 1
The formula for compound interest is : -
FV = P * (1 + (r/100))^ n
Where:- FV = Future Value P = Principal R = Rate of interest n = time.
If you need to compound daily, then divide the rate by the number of periods to get the effective annual rate. To calculate quarterly compounding, the formula would be : - FV = P (1+(r/4))^4
To calculate daily compounding, replace 4 with 365.
Once you get the effective rate, you can replace it in the original formula(The first one mentioned) and get the exact future value.