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.
Thank you for your interest in this question.
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