Question

Consider a 20-year mortgage for $392,076 at an annual interest rate of 4.2%. After 5 years, the mortgage is refinanced to an annual interest rate of 2.8%. What are the monthly payments after refinancing?

Answer 1

Monthly payment $ 2,195.76

Step-1:Calculation of monthly payment
Monthly payment	=	Loan amount	/	Present value of annuity of 1
	=	$ 3,92,076.00	/	162.1874
	=	$       2,417.43
Working:
Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.0035)^-240)/0.0035		i	=	4.2%/12	=	0.0035
	=	162.1873927		n	=	20*12	=	240
Step-2:Calculation of mortgage balance after 5 years
Mortgage balance after 5 years	=	Monthly payment	*	Present value of annuity of 1
	=	$       2,417.43	*	133.3777
	=	$ 3,22,430.78
Working:
Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.0035)^-180)/0.0035		i	=	4.2%/12	=	0.0035
	=	133.3777316		n	=	15*12	=	180
Step-3:Calculation of monthly payment after refinancing
Monthly payment	=	Loan amount	/	Present value of annuity of 1
	=	$ 3,22,430.78	/	146.8421
	=	$       2,195.76
Working:
Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.00233)^-180)/0.00233		i	=	2.8%/12	=	0.002333
	=	146.8421351		n	=	15*12	=	180