Mini$-$Project $1$: Mortgage Loan Analysis $(50$ points$)$:

You plan to buy a house in September $2024.$ The sale price is $$580,000.$ You need to pay $15\%$ down payments and borrow the additional $85\%$ from Chase Bank with a $20-$year, $6\mathrm{.}0\%$ fixed$-$rate mortgage loan. You need to pay an equal monthly payment starting from October $1,2024,$ for a total of $20$ years.

$(1)$ Calculate your expected monthly mortgage payment.

$(2)$ Develop the full amortization table for your mortgage loan.

$(3)$ When you prepare your $2024$ tax filing, what is the total mortgage interest payment that you can consider for the tax deduction?

Mini$-$Project $2$: Capital Budgeting Analysis $(50$ points$)$:

A firm is planning a new project that is estimated to yield cash flows of $-$$$35$ million per year in Year $1$ through Year $3,$$$55$ million per year in Years $4$ through $6,$ and $$78$ million in Years $7$ through $8,$ and $$118$ million in Years $9$ through $15.$ This investment will cost the company $$280$ million today $($initial outlay$).$ We assume that the firm's cost of capital is $10\mathrm{.}5\%.$

$(1)$ Draw a timeline to show the cash flows of the project.

$(2)$ Compute payback period, net present value $($NPV$),$ profitability index $($PI$),$ internal rate of return $($IRR$),$ and modified internal rate of return $($MIRR$).$

$(3)$ Discuss whether the project should be taken.