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How will the compounding period (Monthly vs annually) change the discounting formula?

How will the compounding period (Monthly vs annually) change the discounting formula?
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The discount rate is used to determine cash flows. The cash flows occur at the end of each month then we can use the monthly discount formula — the annual discount rate calculated by using the annual percentage rate. The monthly rates can be obtained from dividing the annual rate by 12. But it is different in compounding formula. The conversion of annual rate into monthly rates by compounding we can use the following formula.

APR is the annual percentage rate

The conversion of monthly into annually by using the following formula,

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