Question

Consider a 30-year mortgage for $137018 at an annual interest rate of 3.9%. What is the remaining balance after 19 years? Round your answer to the nearest dollar.

Answer 1

Step-1:Calculation of annual Payment
	Annual Payment		=	Loan Amount / Present Value of annuity of 1
			=	$       1,37,018	/	17.503939
			=	$             7,828
	Working:
	Present Value of annuity of 1			=	(1-(1+i)^-n)/i			Where,
				=	(1-(1+0.039)^-30)/0.039			i	3.90%
				=	17.503939			n	30
Step-2:Calculation of remaining balance after 19 years
	Remaining Balance after 19 Years			=	Annual Payment*Present Value of annuity of 1
				=	$         7,828	*	8.80792
				=	$       68,947
	Working:
	Present Value of annuity of 1			=	(1-(1+i)^-n)/i			Where,
				=	(1-(1+0.039)^-11)/0.039			i	3.90%
				=	8.80792			n	11	(30-19)
Thus,
	Remaining balance after 19 years is			$           68,947