Question

What is the monthly mortgage payment on a $300,000 30 year fixed rate mortgage with an interest rate of 5.125 percent.

A friend who knows you have studied amortization asks your help to find the interest portion of their house payments for tax purposes (assuming they itemize). The monthly payments are $2,107.02 on a 30 year loan with a 5 percent interest rate.

a) What was the total amount of interest paid during year 2?

b) At what point in time was/will the loan balance be reduced to 50 percent of the original loan amount?

Thank you!

Answer 1

Q1) We are given the following information:

Payment	PMT	To be calculated
Rate of interest	r	5.13%
Number of years	n	30.00
Monthly	frequency	12.00
Loan amount	PV	300000.00

We need to solve the following equation to arrive at the required PMT:

So the monthly Payment is 1633.46

Q2)

A friend who knows you have studied amortization asks your help to find the interest portion of their house payments for tax purposes (assuming they itemize). The monthly payments are $2,107.02 on a 30 year loan with a 5 percent interest rate.

First we need to calculate the loan amount

We are given the following information:

Payment	PMT	2107.02
Rate of interest	r	5.00%
Number of years	n	30.00
Annual	frequency	12.00
Loan amount	PV	To be calculated

We need to solve the following equation to arrive at the required PV

a) We need to create the amortization schedule:

Opening balance = previous year's closing balance
Closing balance = Opening balance-Principal repayment
PMT is calculated as per the above formula
Interest = 0.05 /12 x opening balance
Principal repayment = PMT - Interest
So the total interest in year two is the sum of interest payments for months 13 to 24 which comes to $19,197.18

b) The closing balance is  $1,96,088.76 after 242 payments which is almost the close to 50% of the loan amount so it will take 242/12 = 20.167 or 20 years 2 months to recover 50% of the loan amount