# How is the value of the amount to be repaid estimated when an amount is borrowed?

## Expert Answers In the case of complex interest, interest in any cycle is paid on both the initial amount borrowed as well as the interest accumulated till the cycle before that.

For an amount borrowed equal to P at a per cycle rate of interest i and for a period equal to n (i.e. n cycles), the total repayment to be paid is equal to P*(1 + i)^n. An example that illustrates the importance of the per cycle rate of interest and the number of cycles is when compounding is done every month. Here, if the annual rate of interest is i, the monthly rate of interest is i/12 but the number of cycles increases from 1 to 12 in a year.

The total repayment for an amount borrowed equal to A, at a rate of interest i and for a period n is equal to P*(1 + i)^n

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