You are going to make the decision about which mortgage to consider by calculating the NPV of switching from the no$-$fee mortgage $($benchmark$)$ to each of the top six mortgage listed $($sorted by their coupon$).$

To calculate NPV of this decision, calculate the difference in payments today, and over the life of the mortgage, by subtracting the alternative mortgage payments from the no$-$fee mortgage payments and calculating NPV$.$ Assume that you will be living in the house for the next $30$ years for certain and you will never repay the mortgage early. Which mortgage should you undertake?

$1-(1)$ In the basic information of the table, Monthly Rate was calculated by dividing Rate $(\%)$ by $1200.$ Why?

$1-(2)$ Find the monthly payment of the mortgage. You can apply the formula for PV of Annuity $($Chapter $4).$

$1-(3)$ Find the difference between Benchmark and Alternative with respect to Upfront Payment and Monthy Payment of Mortgage. For example, if an alternative has upfront cost $$100,$ the difference will be $-100.$ Be careful about the unit of Monthly Rate and Points. Read the footnote of the case about how to calculate upfront cost.

$1-(4)$ Find Net Present Value $($NPV$)$ of Alternative products based on $1-(3).$ You can apply the formula for PV of Annuity $($Chapter $4).$ Be careful about your discount rate.

$\backslash$table$[[$Loan Amount,$$400,000$