Loan repayment calculations when interest compounding frequency does not match repayment frquency Is there a formula for calculating loan repayments where interest is compounded daily, but repayments are made only monthly, for instance?
I would like to be able to calculate the repayment amount for any combination of repayment and compounding frequencies.
Cheers!

Let


*

*$P$ = the principal amount

*$n$ = the number of compounding periods that fit into each repayment period = e.g., 30 days in a month, in your case

*$r$ = the interest rate over the compounding period = a daily interest rate in your case, expressed as a decimal, e.g. 0.1% expressed as 0.001


The principal outstanding at the end of the repayment period is
$$P\left( 1+ r  \right)^n$$
So the interest paid is the outstanding principal less the original principal
$$P\left( 1+ r  \right)^n - P$$
