Question

A borrower takes out a 30-year mortgage loan for $250,000 with an interest rate of 6% and monthly payments. What portion of the first month's payment would be applied to interest? ($1250) Assume the question above was a negative amortization loan, what would be the balance after 3 years?

Answer 1

a.	First month payment applied to interest		$       1,250.00
Working:
	Interest expense	=	Loan balance at the beginning	*	Monthly interest rate
		=	$ 2,50,000.00	*	6%*1/12
		=	$       1,250.00
b.	Balance after 3 years		$ 2,40,210.18
Working:
	Present value of annuity of 1 for 360 months	=	(1-(1+i)^-n)/i		Where,
		=	(1-(1+0.005)^-360)/0.005		i	=	6%/12	=	0.005
		=	166.7916144		n	=	30*12	=	360
	Monthly payment	=	Loan amount	/	Present value of annuity of 1
		=	$ 2,50,000.00	/	166.7916
		=	$       1,498.88
	Present value of annuity of 1 for 324 months	=	(1-(1+i)^-n)/i		Where,
		=	(1-(1+0.005)^-324)/0.005		i	=	6%/12	=	0.005
		=	160.2601717		n	=	30*12	=	360
	Balance after 3 years	=	Monthly payment	*	Present value of annuity of 1 for 324 months
		=	$       1,498.88	*	160.2602
		=	$ 2,40,210.18