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.
asked Aug 10, 2015 at 12:27
-
1Are you sure you need to use APR ? Wouldn't you be using the interest rate ?– DumbCoderCommented Aug 10, 2015 at 12:49
-
yes I think your right– Barry HamiltonCommented Aug 10, 2015 at 12:54
-
I found this article helpful: calculate.onl/convert-annual-interest-rates– Nathan ArthurCommented Oct 11, 2020 at 11:51
Add a comment
|
2 Answers
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
answered Aug 10, 2015 at 15:40
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.
