Please, show all your work. Good Luck!

Problem points$]$:

On January $1,$ Sophia Smith signed a three$-$year contract to work for a computer software

company. She will be paid $$10,000$ at the end of each month and a bonus of $$20,000$ at each

year$-$end. What is the present value of the contract if the stated annual interest rate, compounded

monthly, is $12$ percent?

Problem points$]$:

You just graduated from MSUM MBA and got a nice job offer. You want to lease a set of golf

clubs from Pings Ltd$.$ The lease contract comprises $24$ equal monthly payments at a $12$ percent

annual interest rate, compounded monthly. Since the clubs cost $$4,000$ retail, Pings wants the PV

of the lease payments to equal $$4,000.$ Suppose that your first payment is due immediately. What

will your monthly lease payments be$?$

Problem points$]$:

Joe Barta wants to save money to meet two objectives: First, he wants to retire $31$ years from

today with a retirement income of $$300,000$ per year for $20$ years. The first retirement payment

will occur $31$ years from today. Second, he would like to purchase a cabin in the mountains $10$

years from today at an estimated cost of $$350,000.$ He can afford to say only $$40,000$ at the end

of each year for the first $10$ years. He expects to earn $7$ percent per year on his savings.

Assuming he saves the same amount each year, what must Joe save annually at the end of year

$11$ through year $30$ to meet his objectives?