Four years ago, Emily secured a bank loan for $200,000 for the purchase of a hou

Question

Four years ago, Emily secured a bank loan for $200,000 for the purchase of a house. The term of the mortgage is 30 years , with an interest rate of 9.5%/year compounded monthly. Because the interest rate for a conventional 30-year mortgage has now dropped to 6.75%/yearly compounded monthly, Emaily is thinking of refinancing her property. a.what is emilys current monthly mortgage payment? b.What is emilys current outstanding principle? c.If Emily decides to refinance her property by securing a 30 year home mortgage loan in the amount of the current outstanding principle at the prevailing interest rate of 6.75%/yearly compounded monthly, what will be her monthly mortgage payment? d.How much less would Emily monthly mortgage payment be if she refinances?

Explanation / Answer

Let us calculate sum, 'a' of mortgage loan to be paid each month.
monthly rate = 0.095/12 = 0.0079167
no. of months = 30X12 = 360
a) Loan $200000 = a(1.007917^360-1)/(0.007917*1.007917^360)
a = 1681.06

b) PV of payments at the end of 8 years i.e. 96 months
= 1681.06*(1.007917^96 -1)/(0.007917*1.007917^96)
= 112738.86
Principal due = 200000 - 112738.86 = 87261.145

c) monthly payment = 87261.145[0.007917*1.007917^360]/[1.007919^360 -1]

= 733.76

d) 1681.06 -  733.76 = 947.3

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