Question

You want to buy your dream house by borrowing $300,000 for 15 years, with monthly payments. The bank quotes a fixed rate of 5.5%. What is the total interest you paid by the end of the 5^th year?

Answer 1

Total interest you paid by the end of the 5^th year is $ 72,942.01

Step-1:Calculation of Monthly payment
Monthly payment		=	Loan amount	/	Present value of annuity of 1
		=	$       3,00,000	/	122.3865193
		=	$       2,451.25
Working:
Present value of annuity of 1		=	(1-(1+i)^-n)/i		Where,
		=	122.3865193		i	5.5%/12	=	0.00458333
					n	15*12	=	180
Step-2:Calculation of loan amount at the end of year 5
Loan amount is the present value of monthly payment.
Loan amount at the end of year 5		=	Monthly payment	*	Present value of annuity of 1 for 10 years
		=	$       2,451.25	*	92.14358207
		=	$ 2,25,866.99
Working:
Present value of annuity of 1 for 10 years		=	(1-(1+i)^-n)/i		Where,
		=	92.14358207		i	5.5%/12	=	0.00458333
					n	10*12	=	120
Step-3:Calculation of interest payment in year 5
Total payment by the end of 5th year			$ 1,47,075.02
Less loan repayment by the end of 5th year			$     74,133.01
Total interest paid by the end of 5th year			$     72,942.01
Working:
Total payment by the end of 5th year		=	$       2,451.25	*	5	*	12	=	$ 1,47,075.02
Loan repayment by the end of 5th year		=	Loan amount the beginning	-	Loan amount at the end of year 5
		=	$       3,00,000	-	$ 2,25,866.99
		=	$     74,133.01