## PRORATION—WORKING INSIDE A COMPOUNDING INTERVAL

Suppose I want to pay off a loan 4 months and 20 days after taking the loan.[7] The bank isn’t going to just use the results of the fourth compounding interval calculation and give me the interest they earned in the last 20 days. On the other hand, I don’t think it’ s fair for the bank to use the fifth compounding interval calculation and charge me 10 days’ worth of interest that the bank hasn’t earned.

Let’s say that there are 30 days in the current month. Take the interest rate per

month ^ R j and divide it by 30, giving us an interest rate per day, then we multiply

this by the number of days, giving us an effective interest rate for the 20 days of the month:

The interest is just the above number times the balance after 4 months...

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