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How can interest be compounded quarterly but with payments made on a monthly basis? Can you give me an example?

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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 %

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