Amortization. A woman buys house for $200,000. She makes a $50,000 down payment

Question

Amortization. A woman buys house for $200,000. She makes a $50,000 down payment and amortizes the rest of the purchase price with monthly payments over the next 30 years with an annual interest rate of 4% compounded monthly. What is the size of each monthly payment? How much of the first payment is interest? (Remember that the first payment includes the interest due from holding $200,000 for one month.) How much does she still owe after making the first payment? What is the total amount of money she will have paid over the life of the loan? What is the total interest she will have paid over the life of the loan? a. b. c. d. e.

Explanation / Answer

Find the monthly payment

Periodic payment of a loan is given by

P = L[r(1 + r)^n]/[(1 + r)^n - 1]

P - Periodic payment = ?

r - Interst rate = 0.04/12 = 0.003333333

n - Term = 30*12 = 360

L - Loan amount = 200000 - 50000 = 150000

P = 150000*(0.003333333(1 + 0.003333333)^360)/((1 + 0.003333333)^360 - 1) = 716.12

Monthly payment = $716.12

b.

First payment interest component = Loan * interest = 150000*0.04/12 = $500

c.

Principal component in the first payment = payment - interest = 716.12-500 = $216.12

Loan balance = 150000 - 216.12 = $149283.88

d.

Total amount = 716.12*360 = $257804.26

e.

Total interest = Total paid - Loan = 257804.26 - 150000 = $107804.26

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