Question

A couple has just purchased a home for $348,400.00. They will pay 20% down in cash, and finance the remaining balance. The mortgage broker has gotten them a mortgage rate of 5.04% APR with monthly compounding. The mortgage has a term of 30 years. How much interest is paid in the first year?

Answer 1

$13,954.04

Working:

Monthly Payment		=	Loan Amount/cumulative disocount factor
		=	$ 2,78,720.00	/	185.43624
		=	$       1,503.05
Working:
Loan Amount		=	$ 3,48,400.00	x	(1-0.20)	=	$ 2,78,720.00
Cumulative discount factor		=	(1-(1+i)^-n)/i			Where,
		=	(1-(1+0.0042)^-360)/0.0042			i	5.04%/12	=	0.0042
		=	185.43624			n	30*12	=	360
Amortization Schedule for first year (12 months)
Months	Beginning		Monthly Payment		Interest expense		Reduction in principal		Ending
	Loan Balance								Loan Balance
	a		b		c=a*5.04%/12		d=b-c		a-d
1	$ 2,78,720.00		$       1,503.05		$               1,170.62		$           332.43		$ 2,78,387.57
2	$ 2,78,387.57		$       1,503.05		$               1,169.23		$           333.82		$ 2,78,053.75
3	$ 2,78,053.75		$       1,503.05		$               1,167.83		$           335.22		$ 2,77,718.53
4	$ 2,77,718.53		$       1,503.05		$               1,166.42		$           336.63		$ 2,77,381.89
5	$ 2,77,381.89		$       1,503.05		$               1,165.00		$           338.05		$ 2,77,043.85
6	$ 2,77,043.85		$       1,503.05		$               1,163.58		$           339.47		$ 2,76,704.38
7	$ 2,76,704.38		$       1,503.05		$               1,162.16		$           340.89		$ 2,76,363.49
8	$ 2,76,363.49		$       1,503.05		$               1,160.73		$           342.32		$ 2,76,021.17
9	$ 2,76,021.17		$       1,503.05		$               1,159.29		$           343.76		$ 2,75,677.40
10	$ 2,75,677.40		$       1,503.05		$               1,157.85		$           345.21		$ 2,75,332.20
11	$ 2,75,332.20		$       1,503.05		$               1,156.40		$           346.66		$ 2,74,985.54
12	$ 2,74,985.54		$       1,503.05		$               1,154.94		$           348.11		$ 2,74,637.43
Total			$     18,036.60		$            13,954.04		$       4,082.57