Suppose that you are currently making monthly payments on a $200,000 30 year mor

Question

Suppose that you are currently making monthly payments on a $200,000 30 year mortgage at 3.95805% interest compounded monthly. For the last 18 years, you have been paying the regular monthly payments. You now have the option to refinance your current mortgage with a new 15 year mortgage that has an interest rate of 3.3592167% compounded monthly. Note that the lender of the new loan has a closing cost fee of $1,000 (for title insurance, home appraisal, etc.) for the new (refinanced) mortgage. The lender stipulates that the closing cost must be paid in cash and cannot be part of the new loan. Taking the closing cost into account, determine whether you would save or lose money, in interest, if you were to refinance your home.

Explanation / Answer

EMI =P*r*(1+r)n/((1+r)n-1)

= 200000*.0395805*(1+.0395805)360/((1+.0395805)360-1)

= $950

Total payment of EMI Amount remaining = 950*144= $ 136800

PV of mortgage payment Remaining = 950*pvifa((3.95805%/12),144)

=108758.75

So interest payment =136800 - 108758.75 = $28,041.25

New EMI in refinance = $770

Total Payment under new EMI = $ 770* 15years * 12 month = $138600

Interest paid in refinance = 138600 - 108758.75 = $29841.25

so Extra Payment of interest in refinance = 29841.25- 28041.25 =1800.01

Closing cost = $1000

So total Extra payment under refinance = 2800.01

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