smh@mhuxl.UUCP (henning) (11/25/85)
**** **** From the keys of Steve Henning, AT&T Bell Labs, Reading, PA mhuxl!smh If r is the interest per payment period, x is the payment, n is the number of payments and p is the principle Richard Schooler derived: > x = p * r * (1 + 1 / ((1 + r)^n - 1)). > n = log (1 + (p * r) / (x - (p * r))) / log (1 + r). Note: these equations have problems with interest free loans where r=0, x=p/n, and conversely n=p/x Since these are trivial cases, congratulations Rich on a fine solution. > If we now set x and r to half the previous amounts to model paying > half a monthly payment twice a month, we get n = 718, or almost exactly > 30 years, so we aren't saving much. If we follow someone else's suggestion, > and pay the half-monthly amount every two weeks, then this is equivalent > to paying 13/12 ths the monthly amount every month, so x = $1114.33. > Keeping r = .01, we get n = 228 months, or 19 years. Carrying this one step further we find that for various interest rates we get: r= 7% 8% 9% 10% 11% 12% 13% 14% 15% n= 23.73 22.85 21.92 20.96 20.00 19.04 18.08 17.19 16.13 years respectively on a 30 year mortgage with 1/2 of the monthly payment paid biweekly. Going one more step, for various year mortgages at 11% interest we get: old n= 30 years 25 years 20 years 15 years 10 years old x= $952.32 $980.11 $1032.18 $1136.60 $1377.50 new n= 20.0 yrs 18.15 yrs 15.62 yrs 12.46 yrs 8.69 yrs respectively on a 30 year mortgage where the new biweekly x is 1/2 of the old monthly x.