Question

You are about to buy a million dollar house with a 20 percent down payment. The mortgage has 5 percent stated annual interest rate, compounded monthly, and calls for equal monthly payments over the next 30 years. The first payment is due one month from now. What is your monthly mortgage payment?

I know the answer si 4294.57

but I am having trouble understanding the second part of the question

The mortgage terms require that at the end of year 7 you prepay the mortgage, that is pay the present value of the subsequent payments. How much will you have to pay 7 years from now?

What is this asking exactly and how do I approach this?

Answer 1

Loan taken = 80% of $1 million = $800,000

Annual interest = 5% per annum

Monthly interest = 5%/12 = 0.416%

No. of periods = 12*30 = 360 months

Let monthly mortgage payment be x

800,000 = x/(1+0.416%) + x/(1+0.416%)^2 + .... + x/(1+0.416%)^360

x=$4294.57

At the end of 7 years, PV of all future payments = Y. No. of periods remaining = 23*12 = 276

Y = x/(1+0.416%) + x/(1+0.416%)^2 + .... + x/(1+0.416%)^276; where x=$4294.57

Using PV function in excel where rate = 0.416%, nper=276, pmt=4294.57, fv=0, type = 0, we get Y = $704,086.18 which will be the prepayment amount for subsequent 23 years.