# converting annual interest rate to monthly when compounding frequency known

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, `m`:

``````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, `m`:

``````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.