Question

A fully amortizing mortgage loan is made for $100,000 at 4.5% for 30 years. Payments will be made monthly.
Calculate the following:
a. Monthly payments
b. Interest and principal payments during month 1.
c. Total interest and principal payments made over the life of the loan (30 years).
d. If the property were sold at the end of year 15, how much is still owed on the mortgage?
e. At the end of year 15, how much has been paid in interest and principal in total?

Answer 1

a]	LOAN AMORTIZATION FORMULA
	PMT = L*r*(1+r)^n/((1+r)^n-1), where
	PMT = Periodic payment [installment]
	L = Loan amount
	r = interest rate per month
	n = number of months
	Monthly payments = 100000*(0.00375)*(1.00375)^360/(1.00375^360-1) =	$              506.69
b]	Interest during the 1st month = 100000*0.00375 =	$              375.00
	Principal during the 1st month = 506.69-375 =	$              131.69
c]	Total amount paid = 506.69*360 =	$      182,408.40
	Total principal payment over the life of the loan	$      100,000.00
	Total interest payment over the life of loan	$        82,408.40
d]	Amount owed at EOY 15 = PV of remaining 180 installments = 506.69*(1.00375^180-1)/(0.00375*1.00375^180) =	$        66,234.57
e]	Total amount paid = 506.69*180 =	$        91,204.20
	Total principal paid = 100000-66234.57 =	$        33,765.43
	Total interest paid	$        57,438.77