3

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.

  • 1
    Are you sure you need to use APR ? Wouldn't you be using the interest rate ? – DumbCoder Aug 10 '15 at 12:49
  • yes I think your right – Barry Hamilton Aug 10 '15 at 12:54
3

Probably simplest to convert to effective annual rate first:

link:- Effective Annual Rate - Calculation

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
2

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.

You must log in to answer this question.

protected by Chris W. Rea Mar 12 at 23:29

Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count).

Would you like to answer one of these unanswered questions instead?

Not the answer you're looking for? Browse other questions tagged .