• pmt(rate, nper, pv, [[fv], [type]])—Returns the payment for an investment or loan based on periodic, constant payments over a given number of compounding periods nper using a fixed interest rate and a specified present value pv.

• ppmt(rate, per, nper, pv, [[fv], [type]])—Returns the payment on the principal of an investment or loan for a given period per based on periodic, constant payments over a given number of compounding periods nper using a fixed interest rate and a specified present value.

• ipmt(rate, per, nper, pv, [[fv], [type]])—Returns the interest payment of an investment or loan for a given period per based on periodic, constant payments over a given number of compounding periods nper using a fixed interest rate and a specified present value.

• rate is the real, positive, scalar fixed interest rate per period. Typically, 0 ≤ rate < 1.

• nper is the positive integer number of compounding periods.

• pv is the real, positive present (or initial) value loan.

• fv (optional) is the future value: a cash balance you want to attain after the last payment is made. If omitted, fv = 0.

• type (optional) is 0 for a payment made at the end of the period or 1 for the beginning. If omitted, type = 0.

• per is the positive integer period to find interest. per ≤ nper.