Mortgage Options Analysis

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Mortgage Options Analysis

You decided to buy a house in Amherst valued at $250,000 and need to borrow the entire amount to finance your house. After shopping around for a mortgage loan, you found that the following two deals from the Mortgage One Company are very attractive:
Option 1: A 15-year fixed rate mortgage with no point and an APR of 5%, compounded monthly.
Option 2: A 15-year fixed rate mortgage with two points and an APR of 4.5%, compounded monthly.
The closing costs (not including the points) for the two loans are identical.
According to the law, the interests on your mortgage payments are tax deductible. In fact, at the end of each year, your lender will simply add up your 12-month interest payments (without
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These annual amounts I used to calculate annual tax savings by multiplying annual interest amount by tax rate. In order to be able to compare the amounts received in different years, I found present values of each cash flow. I added up the PVs of tax savings for every year to get total tax savings (all 15 years for option 1 and first 5 years for option 2).
For option 2 I calculated the savings I receive from reduced payment. For that I used difference between the mortgage payments as annuity payment for 180 months for Question A and for 60 months for Question B
For option 2 I also calculated the tax savings from points by multiplying amount paid for points by tax rate. Since the tax savings occurred in the end of the year I discounted that amount for 1 year.
For option with refinance, I completed similar calculations as in options 1 and 2. However, for the first 5 years the payment was as in option 1. Then, I calculated new payment for years 11-15 by using ending balance after 60 months as new loan amount; I used APR of 4.25% compounded monthly. Then, I found present values of tax savings. In this case, present time is after 60 month in house. When
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