Question

You have just bought a house and have a $125,000, 25-year mortgage with a fixed interest rate of 8.5 percent with monthly payments. Over the next five years, what percentage of your mortgage payments will go toward the repayment of principal?.

Answer 1

Mortgage loan amount is always present value of monthly payments.
Step-1:Calculation of monthly payment
Monthly Payment		=	Loan amount	/	Present value of annuity of 1
		=	$       1,25,000	/	124.192727
		=	$       1,006.50
Working:
Present value of annuity of 1		=	(1-(1+i)^-n)/i		Where,
		=	(1-(1+0.007083)^-300)/0.007083		i	8.5%/12	=	0.007083
		=	124.1927274		n	25*12	=	300
Step-2:Calculation of prinicipal repayment over next 5 years
Principal repayment over next 5 years		=	Monthly Payment	*	Present value of annuity of 1
		=	$       1,006.50	*	48.7416406
		=	$     49,058.47
Working:
Present value of annuity of 1		=	(1-(1+i)^-n)/i		Where,
		=	(1-(1+0.007083)^-60)/0.007083		i	8.5%/12	=	0.007083
		=	48.74164062		n	5*12	=	60
Step-3:Calculation of percentage of payment towards principal
Total Repayment of loan over next 5 years		=	$       1,006.50	*	60	=	$ 60,390.01
Loan repayment							$ 49,058.47
Percentage of principal repayment towards loan		=	$     49,058.47	/	$ 60,390.01	=	81.24%