Their example applied to the formula for d s = 4329.58 See also Calculating the Present Value of an Ordinary Annuity where they show If the APR is an effective annual rate use r = (1 + APR)^(1/12) - 1 to obtain the monthly rate.Īn expression can be obtained for the periodic payment d s = (d - d (1 + r)^-n)/r R is the periodic interest rate, so if the APR is a nominal annual rate compounded monthly r = APR/12. The summation can be converted to a formula by induction, so The mathematics on which the usual formula is based is that the sum of the payments d, each discounted to present value (PV) by 1/(1 + r)^k, should equal the initial (present value) value of the loan s.