Question

# You took out your home mortgage five years ago, and are currently considering refinancing into a...

You took out your home mortgage five years ago, and are currently considering refinancing into a loan at a lower rate and for a shorter term. Your original loan was for 30 years, at 6% interest on the \$200,000 borrowed, and you pay monthly. The new loan you are considering will be for 15 years at a rate of 4%. Again, the payments will be monthly. What will your new payment be if you take on this new loan? SHOW STEP.

The mothly rate on the existing loan is 6/12 = 0.5%. We first calculate how much was the monthly payment and how much we have already paid. The monthly payment will be calculated as: 200,000 = A x (1/1.005 + 1/1.005^2 + ... + 1/1.005^360). Hence, A = 1199.1.

So, the amount we have already paid will be = 1199.1 x (1/1.005 + 1/1.005^2 + ... + 1/1.005^60) = 62024.12. So, the remaining amount is = 200,000 - 62,024.12 = 137975.9

Hence, doing the same procedure, let the new monthly payment be B. The new interest rate will be 4/12 = 1/3% = 0.00333.

137975.9 = B (1/1.0033 + 1/1.0033^2 + ... + 1/1.0033^(15 x 12))

Hence, B = 1020.591

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