Part I: Obtain current mortgage rates

Assume you plan to purchase a $$600,000$ home with a $20\%$ down payment. You need to obtain quotes of current mortgage rates on $30-$year fixed rate mortgage, with and without discount points, from at least three mortgage lenders. Please record your findings in your report.

Part II: Calculate and analyze mortgage payments

Based on the obtained quotes, you choose two best quotes: one with discount points and another without points. Please perform similar analyses as discussed in class. First, please use the mortgage rate without points for the first three questions.

$(1)$ What is your monthly payment?

$(2)$ If you make regular monthly payments, how long will it take to pay off half of the loan? $($i$.$e$.,$ reduce the principle of the loan balance to half$)$

$(3)$ After making regular monthly payments for $10$ years, how much will be the loan balance?

Next, please compare the mortgage payment based on your chosen mortgage rate with discount points. To obtain consistent results, please use quotes with and without points from the same lender. Please complete the analyses for the following three questions.

$(4)$ For the chosen mortgage loan with discount points, how much do you need to pay for the points?

$(5)$ What is the NPV of paying the points? $($i$.$e$.,$ the PV of savings in monthly payments over the life of the mortgage loan net of the initial payment for points$)$

$(6)$ How long must you stay in the house to make it worthwhile to pay the points to lower down the interest rate, assuming the savings in payments can be reinvested at the same rate?