Question

You are considering two payment options on a $500,000 20-year mortgage having an interest rate of 2.8% compounded monthly. The first option is to make monthly payments at the start of each month, while the second option is to make payments at the end of each month. How much interest will be saved by choosing the first option ?

Answer 1

Step 1 :	Monthly payment under first option
	Present Value Of An Annuity Due
	=C + C*[1-(1+i)^-(n-1)]/i]
	Where,
	C= Cash Flow per period
	i = interest rate per period
	n=number of period
	500000= C+C[ 1-(1+0.002333333)^-(240-1) /0.002333333]
	500000= C+C[ 1-(1.002333333)^-239 /0.002333333]
	500000= C+C[ (0.4271) ] /0.002333333
	C = 2716.86
	Monthly payment = $2716.86
Step 2:	Monthly payment under Second option
	Present Value Of An Annuity
	= C*[1-(1+i)^-n]/i]
	Where,
	C= Cash Flow per period
	i = interest rate per period
	n=number of period
	500000= C[ 1-(1+0.00233333)^-240 /0.00233333]
	500000= C[ 1-(1.00233333)^-240 /0.00233333]
	500000= C[ (0.4284) ] /0.00233333
	C = 2723.19
	Monthly payment = 2723.19
Step 3 :	Interest saved
	= Total Payment under option 2 - total payment under option 1
	= ($2723.19*240)-($2716.86*240)
	=1519.20
	= Or 1521.23 ( if no intermediate rounding off)