$4.$ 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?

Please no excel usage, show formulas