How can interest be compounded quarterly but with payments made on a monthly basis? Can you give me an example?
1 Answer
The monthly basis calculation uses a rate converted from the quarterly compounded rate. For example 10% per annum compounded quarterly, q
q = 0.10
effective annual rate, r = (1 + q/4)^4 - 1 = 0.103813
See Effective interest rate calculation
monthly rate, m = (1 + r)^(1/12) - 1 = 0.826484 %
$100 compounded monthly for 12 months
$100 (1 + m)^12 = $110.38
Or compounded quarterly for 4 quarters
$100 (1 + q/4)^4 = $110.38
Finally, same rate expressed as a nominal annual rate compounded monthly
12 m = 9.91781 %