Question

I have a choice between two different fixed-rate mortgages when I purchase my $150,000 house. One is a 20-year mortgage with a quoted rate of 4.375% and the other is a 30-year mortgage with a quoted rate of 4.5%. Both rates are monthly compounded, and both mortgages require equal monthly payments. What is the required monthly payment of each loan? How much of a down payment would I have to make if I wanted the 20-year loan’s payment to be that of the 30-year loan payment (with no down payment)?

Answer 1

Monthly payment in option 1	Using pmt function in MS excel	pmt(rate,nper,pv,fv,type) rate = 4.375/12 =.364% nper = 12*20 =240 pv = 150000 fv =0 type =0	PMT(0.3645%,240,150000,0,0)	($938.80)
Monthly payment in option 2	Using pmt function in MS excel	pmt(rate,nper,pv,fv,type) rate = 4.5/12 =.375% nper = 12*30 =360 pv = 150000 fv =0 type =0		($760.03)
present value of 20 year loan on a payment of 760.3	Using present value function in MS excel	pv(rate,nper,pmt,fv,type) rate = .364% nper = 240 pmt = -760.3 fv =0 type =0	PV(0.364%,240,-760.03,0,0)	$121,498.59
down payment	150000-121498.59	28501.41