Question

1. Cliff has owned his home for 15 years and expects to live in it for 5 more years. He originally borrowed $150,000 at 5% for 30 years to buy the home. He still owes $110,000 on the loan. Interest rates have fallen to 4% and Cliff wants to know if he should refinance the loan for 15 years. He would pay 2 points on the new loan with no prepayment penalty on the existing loan.
2. What is Cliff’s current monthly payment?
3. Calculate the monthly payment on the new loan.
4. Should Cliff refinance or not?  

Answer 1

(a) Original Mortgage: Mortgage Value = $ 150000, Interest Rate = 5 % , Tenure = 30 years or (30 x 12) = 360 months

Applicable Monthly Rate = 5 / 12 = 0.4167 %

Let the monthly repayments be $ n

Therefore, 150000 = n x (1/0.004167) x [1-{1/(1.004167)^(360)}]

150000 = n x 186.273

n = 150000 / 186.273 = $ 805.269 ~ $ 805.27

(b) New Mortgage Amount = Outstanding Mortgage + 2 points = 110000 + 0.02 x 110000 = $ 112200

Interest Rate = 4 %, Tenure = 15 years or (15 x 12) = 180 months

Applicable Monthly Rate = 4 / 12 = 0.33 %

Let the monthly repayments be $ m

Therefore, 112200 = m x (1/0.0033) x [1-{1/(1.0033)^(180)}]

112200 = m x 135.56

m = 112200 / 135.56 = $ 827.68

(c) As is observable, the home buyer pays less periodically in case of refinancing and hence should go for the refinancing option.