Question

Consider a 30-year mortgage for $235,347 at an annual interest rate of 5.1%. After 11 years, the mortgage is refinanced to an annual interest rate of 3.4%. How much interest is paid on this mortgage?

Answer 1

Interest paid on this mortgage is $ 253,138.85

Step-1:Monthly payment over 11 years
Monthly payment	=	Loan amount	/	Present value of annuity of 1
	=	$ 2,35,347.00	/	184.1791
	=	$       1,277.82
Working;
Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	184.1790989		i	=	5.1%/12	=	0.00425
				n	=	30*12	=	360
Step-2:Remaining loan balance after 11 years
Loan amount	=	Monthly payment	*	Present value of annuity of 1
	=	$       1,277.82	*	145.8253
	=	$ 1,86,337.97
Working;
Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	145.8253495		i	=	5.1%/12	=	0.00425
				n	=	(30-11)*12	=	228
Step-3:New monthly payment
Monthly payment	=	Loan amount	/	Present value of annuity of 1
	=	$ 2,35,347.00	/	167.7822
	=	$       1,402.69
Working;
Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	167.7821894		i	=	3.4%/12	=	0.002833
				n	=	(30-11)*12	=	228
Step-4:Interest payment calculation
Amount repaid over 11 years		$       1,277.82	*	132	=	$ 1,68,671.71
Amount repaid therafter		$       1,402.69	*	228	=	$ 3,19,814.14
Total amount repaid		(a)				$ 4,88,485.85
Mortgage amount		(b)				$ 2,35,347.00
Interest expense		(a) - (b)				$ 2,53,138.85