Question

Consider a 20-year, $115,000 mortgage with a rate of 5.55 percent. Eight years into the mortgage, rates have fallen to 5 percent. What would be the monthly saving to a homeowner from refinancing the outstanding mortgage balance at the lower rate? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Step-1:Calculation of existing monthly payment
	Monthly payment	=	Loan amount	/	Present value of annuity of 1
		=	$ 1,15,000.00	/	144.7776
		=	$           794.32
	Working;
	Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
		=	144.7776479		i	=	5.55%/12	=	0.004625
					n	=	20*12	=	240
Step-2:Calculation of loan balance after 8 years
	Loan balance	=	Monthly payment	*	Present value of annuity of 1
		=	$           794.32	*	104.9624
		=	$     83,373.89
	Working;
	Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
		=	104.9623914		i	=	5.55%/12	=	0.004625
					n	=	12*12	=	144
Step-3:Calculation of revised monthly payment
	Monthly payment	=	Loan amount	/	Present value of annuity of 1
		=	$     83,373.89	/	108.1209
		=	$           771.12
	Working;
	Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
		=	108.1209174		i	=	5%/12	=	0.004167
					n	=	12*12	=	144
Step-4:Calculation of monthly saving
	Monthly payment prior to rate change		$           794.32
	Monthly payment after rate change		$           771.12
	Monthly saving		$             23.20