Question

"Bob got a fully amortizing 30 year fixed rate mortgage with monthly payments for $1,000,000 at an annual interest rate of 4.5%, compounded monthly. If Bob made the required monthly payment every month, how many dollars in interest will Bob pay in his 125th monthly payment?"

		"$1,393.91 "
		"$2,094.63 "
		"$2,972.23 "
		"$35,666.72 "

Answer 1

"$2,972.23 "

Step-1:Calculation of loan repayment in 125th monthly payment
Loan repayment in 125th payment	=	Loan value after 124th payment	-	Loan value after 125th payment
	=	$ 7,92,593.81	-	$ 7,90,499.18
	=	$       2,094.63
Working:
Loan value is always present value of future cash flows.
# 1	Present value of annuity of 1 for 360 months	=	(1-(1+i)^-n)/i		Where,
		=	(1-(1+0.00375)^-360)/0.00375		i	4.5%/12	=	0.00375
		=	197.361159		n	30*12	=	360
# 2	Monthly payment	=	Loan value	/	Present value of annuity of 1 for 360 months
		=	$             10,00,000	/	197.36116
		=	$                5,066.85
# 3	Present value of annuity of 1 for 236 months	=	(1-(1+i)^-n)/i		Where,
		=	(1-(1+0.00375)^-236)/0.00375		i	4.5%/12	=	0.00375
		=	156.4272322		n	(360-124)	=	236
# 4	Loan value after 124th payment	=	Monthly payment	*	Present value of annuity of 1 for 236 months
		=	$                5,066.85	*	156.42723
		=	$          7,92,593.81
# 5	Present value of annuity of 1 for 235 months	=	(1-(1+i)^-n)/i		Where,
		=	(1-(1+0.00375)^-235)/0.00375		i	4.5%/12	=	0.00375
		=	156.0138343		n	(360-125)	=	235
# 6	Loan value after 125th payment	=	Monthly payment	*	Present value of annuity of 1 for 235 months
		=	$                5,066.85	*	156.01383
		=	$          7,90,499.18
Step-2:Calculation of interest expense in 125th monthly payment
	Interest expense	=	Monthly payment	-	Loan repayment
		=	$                5,066.85	-	$ 2,094.63
		=	$                2,972.23