Question

You bought your house five years ago and you believe you will be in the house only about five more years before it gets too small for your family. Your original home value when you bought it was $500,000, you paid 10 percent down, and you financed closing costs equal to 3 percent of the mortgage amount. The mortgage was a 25-year fixed- rate mortgage with a 5 percent annual interest rate. Rates on 30-year mortgages are now at 3 percent. Your total refinancing costs will be 3 percent of the new mortgage amount. A new down payment is not required. Should you refinance?

Answer 1

Downpayment paid = $500000 *10% = $50000

Total Mortgage amount =$450000 + $450000*0.03 =$463500

Monthly Interest rate on current mortgage=0.004167, No of months = 25*12 = 300

Monthly Mortgage payment A is given by

A/0.004167*(1-1/1.004167^300)= 463500

=> A = $2709.57

Principal amount remaining today (5 years after house purchase)

= present value of remaining 240 mortgage payments

=2709.57/0.004167*(1-1/1.004167^240)

=$410569.18

Under Refinancing

New Value of Mortgage = $410569.18 *1.03 =$422886.25

No of months = 30*12 = 360

Interest rate per month = 3%/12 =0.0025

So, Monthly Mortgage payment (X) is given by

X/0.0025*(1-1/1.0025^360)=422886.25

=> X = $1782.91

Since one expects to live only for next 5 years

Under Existing mortgage, principal remaining after 5 years (15 years left to maturity)

=2709.57/0.004167*(1-1/1.004167^180)

=$342639.94

So, the total payments will be $2709.57 every month for next 5 years along with $342639.94 after 5 years to repay the loan completely

Value of these payments at today's interest rates

=2709.57/0.0025*(1-1/1.0025^60)+342639.94/1.0025^60

=$445762.37

As this amount is higher than the amount being financed in the new mortgage ($422886.25). one should refinance the mortgage