$$offered by your local banks, and they provide you with the following offers: The first account offers an annual rate of $7$percent compounded monthly on your investment. The second account offers an annual rate of $7\mathrm{.}25$percent compounded semiannually. As a potential investor, with which account would you choose to invest your money? $(0\mathrm{.}5$pts$)$

$2.$You have recently bought a house for $$250,000,$you paid $10\%$of it as down payment and applied for a $15-$year mortgage to finance the remaining part. The mortgage payment is scheduled at the end of each month. The $15-$year fixed mortgage rate is an annualized rate of $8\%$compounded monthly.

a$)$How much is the monthly payment for this mortgage? $(0\mathrm{.}5$pts$)$

b$)$If the mortgage rate increases to $9\%$how much do the monthly payments increase by $($in dollar terms$)?(0\mathrm{.}5$pts$)$

$3.$You just licensed a piece of software to a large corporation in which you will receive the following payments for the next twenty years. If your discount rate is $12\%$what lump sum of cash received today $($at t $=0)$is equivalent to these future cash flows?

Year$($s$)$Amount received

$1$$$100,000$

$2$$$80,000$

$3$$$60,000$

$4$$$40,000$

$520$$$20,000$

$4.($Note$,$for th$,$ you may find information from the live session in Module $4$useful$.)$Consider the following cash flows of two mutually exclusive projects available for a local business that you are advising. Assume the discount rate for the company is $15$percent$.$ Keep two decimal places when calculating.

Year Project A Project B

$0-$$$200,000-$$$800,000$

$1$$$20,000$$$400,000$

$2$$$60,000$$$400,000$

$3$$$120,000$$$200,000$

$4$$$160,000$$$100,000$

a$)$For each project, Calculate the payback period, the Net Present Value, and the IRR and indicate which project would be selected using that criteria. $(2$pts$)$

b$)$If you can only invest in one of the projects, which is the best one to invest in$?$Briefly explain your reasoning. $(0\mathrm{.}5$pt$)$