Question

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.**

Answer #1

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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