Question

Five years ago you took out a 30-year mortgage with an APR of 6.5% for $200,000. If you were to refinance the mortgage today for 20 years at an APR of 4.25%, how much would your monthly payment change by? (5 points) Your current monthly mortgage payment is $ .(2 decimal places) (5 points) Your current mortgage balance is $ . (1 decimal places) (5 points) Your new monthly mortgage payment would be $ after refinancing. (2 decimal places) (2 points) Your monthly payment will by $

Answer 1

a.	Current monthly mortgage payment	=	Loan amount	/	Present value of annuity of 1
		=	$ 2,00,000.00	/	158.21082
		=	$       1,264.14
	Working:
	Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
		=	158.2108195		i	=	6.5%/12	=	0.005417
					n	=	30*12	=	360
b.	Current Mortgage balance	=	Monthly Payment	*	Present value of annuity of 1
		=	$       1,264.14	*	148.10269
		=	$ 1,87,221.95
	Working:
	Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
		=	148.1026946		i	=	6.5%/12	=	0.005417
					n	=	25*12	=	300
c.	New monthly mortgage payment	=	Loan amount	/	Present value of annuity of 1
		=	$ 1,87,221.95	/	161.48972
		=	$       1,159.34
	Working:
	Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
		=	161.4897183		i	=	4.25%/12	=	0.003542
					n	=	20*12	=	240
d.	Reduction in monthly payment	=	Existing monthly payment	-	New Monthly payment
		=	$       1,264.14	-	$ 1,159.34
		=	$           104.79