• cumint(rate, nper, pv, start, end, [type])—Returns the cumulative interest paid on a loan between a starting period start and an ending period end given a fixed interest rate, number of compounding periods nper, and present value pv of the loan.

• cumprn(rate, nper, pv, start, end, [type])—Returns the cumulative principal paid on a loan between a starting period start and an ending period end given a fixed interest rate, number of compounding periods nper, and present value pv of the loan.

• eff(nrate, npery)—Returns the effective Annual Percentage Rate (APR) given an annual rate nrate and number of compounding periods per year npery.

• 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.

• start and end are the positive integer starting and ending periods of accumulation. start ≤ end ≤ nper.

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

• nrate is the real, positive, scalar nominal annual rate, which, when compounded multiple times per year, yields the APR.

• npery is the positive integer number of compounding periods per year.