Question

Consider the following fixed-rate, level-payment mortgage: maturity = 360 months amount borrowed = $100,000 annual mortgage rate = 10%

(a) Construct an amortization schedule for the first 10 months.

(b) What will the mortgage balance be at the end of the 10th month assuming no prepayments?

Answer 1

(a)	Months	Beginning mortgage loan			Interest Expense		Monthly payment		Reduction in principal			Ending mortgage balance
			a		b=a*10%*1/12		c		d=c-b			e=a-d
	1		$   1,00,000		$     833.33		$     877.54		$    44.21			$ 99,955.79
	2		$ 99,955.79		$     832.96		$     877.54		$    44.58			$ 99,911.21
	3		$ 99,911.21		$     832.59		$     877.54		$    44.95			$ 99,866.27
	4		$ 99,866.27		$     832.22		$     877.54		$    45.32			$ 99,820.94
	5		$ 99,820.94		$     831.84		$     877.54		$    45.70			$ 99,775.24
	6		$ 99,775.24		$     831.46		$     877.54		$    46.08			$ 99,729.16
	7		$ 99,729.16		$     831.08		$     877.54		$    46.47			$ 99,682.69
	8		$ 99,682.69		$     830.69		$     877.54		$    46.85			$ 99,635.84
	9		$ 99,635.84		$     830.30		$     877.54		$    47.24			$ 99,588.60
	10		$ 99,588.60		$     829.90		$     877.54		$    47.64			$ 99,540.96
	Total				$ 8,316.38		$ 8,775.42		$ 459.04
	Working:
	# 1	Present value of annuity of 1			=	(1-(1+i)^-n)/i				Where,
					=	(1-(1+0.008333)^-360)/0.008333				i	10%/12	=	0.008333
					=	113.954658				n			360
	# 2	Monthly Payment			=	Mortgage loan / Present value of annuity of 1
					=	$       1,00,000	/	113.954658
					=	$           877.54
(b)	Mortgage balance be at the end of the 10th month is					$     99,540.96