Question

ENGINEERING ECONOMICS Question 2 When interest rates drop, there are opportunities to refinance an existing mortgage by paying the up front expenses of refinancing and getting a mortgage at a lower interest rate. Whether it is worth doing so or not is a decision that confounds most people. Evaluate concepts of money time relationship principles that need to be considered to make such a decision. Suppose that the original mortgage is a 30 year loan for $200,000 at 8% annual interest compounded monthly. Three years after taking out the original loan, an opportunity arises to refinance and take out a new loan at a 6% annual interest rate which compounded monthly. There is an up front refinancing cost of $2,000 (closing costs) plus 2% of the new loan amount. Prepare a report which you will submit to the board of director of your company for explaining your decision. The report should consist of all detailed calculations and illustrations of the concepts by way of graphs, diagrams, charts, and other visual aids with the appropriate explanation of your economic analysis.

Answer 1

The loan amount is $200000 and interest rate is 8% with tenure of 30 years.
We need to calculate the EMI here.

=PMT(8%/12,360,-200000)
= 1467.53

After 3 years,
Total interest paid
=CUMIPMT(8%/12,360,200000,1,36,0)
= 47391.35

Total principal paid
=CUMPRINC(8%/12,360,200000,1,36,0)
= 5439.70

Total interest payable in this mortgage
=CUMIPMT(8%/12,360,200000,1,360,0)
= 328310.49

Principal Balance after 3 years
200000 - 5439.70 = 194560.30

This is the new principal and new interest rate is 6%.
Upfront fees include $2000 and 2%of loan amount

2000 + (194560.30 * 0.02) = 5891.21

If the tenure for the new mortgage is 30 years then
=CUMIPMT(6%/12,360,194560.3,1,360,0)
= 225375.13

FV of the upfront cost
=FV(6%/12,360,,-5891.21)
= 35480.26

The total FV of savings

328310.49 - 225375.13 - 35480.26 = 71105.03

The refinancing option is beneficial in this case.