Solve using a financial calculator:

$1.$ Brad and Wendy put $$1,800$ into a college fund every year for their son, Jack, on his birthday, with the first deposit one year from his birth $($at his very first birthday$).$ The college fund has a guaranteed annual growth or interest rate of $4\mathrm{.}75\%.$ At his eighteenth birthday, they will pay the last $$1,800$ into the fund. How much will be in the college fund for Jack immediately following this last payment? $(4$ points$)$

$2.$ Bart Simpson, age $10,$ wants to be able to buy a really cool new car when he turns $16.$ His really cool car costs $$18,000$ today, and its cost is expected to increase $2\mathrm{.}5$ percent annually. Bart wants to make one deposit today into an account paying $6\mathrm{.}45$ percent annually in order to buy his car in $6$ year. How much will Bart$$s car cost, and how much does Bart have to save today in order to buy this car at age $16.(5$ points$)$

$3.$ A smooth used$-$car salesman is offering you a great deal on a $$preowned$$ car. He says, $$For only five annual end$-$of$-$the year payments of $$2,180,$ the beautiful $2016$ Honda Civic can be yours.$$ If you can borrow money a $5\mathrm{.}47\%,$ what is the price of the car? If you are to make the payment at the beginning of the year, what is the price of the car? $(5$ points$)$

$4.$ In March $2014,$ Warren Buffett, one of the most successful investors and the CEO of Berkshire Hathaway Inc. offered $$1$ billion for the winner who has a perfect March madness Bracket. The winner has two choices:

A$)$ Receive $40$ annual payments of $25$ million each $($assume beginning$-$of$-$ the$-$year payments$)$

B$)$ Receive a lump sum payment today of $$500$ million immediately

a$.$ Draw the time lines for the two choices.

b$.$ Find the FV $($at the end of year $40)$ of the two choices assuming interest rate is $8\%?$ Which choice should the group select?

c$.$ Find the PV of the two choices assuming interest rate is $8\%.$ Which choice should the group select?

d$.$ Find the FV $($at the end of year $40)$ for the two choices assuming interest is $4\%.$ Which choice should the group select?

e$.$ Find the PV of the two choices assuming interest rate is $4\%.$ Which choice should the group select? $(10$ points$)$