Your brother has offered to give you $$100,$ starting next year, and after that growing at $2\mathrm{.}7\%$ per year for the next $20$ years. You would like to calculate the value

of this offer by calculating how much money you would need to deposit in a local bank so that the amount will generate the same cash flows as he is offering

you. Your local bank will guarantee a $5\mathrm{.}6\%$ annual interest rate so long as you have money in the account.

a$.$ How much money will you need to deposit into the account today?

b$.$ Assuming you deposited the amount of money in part $($a$),$ and then withdrew the required payments each year, calculate the remaining balance at the end of

years $1,2,10$ and $19.($Hint: To solve this problem it is best to use an excel spreadsheet.$)$

a$.$ How much money will you need to deposit into the account today so that the account will generate the same cash flows as he is offering you?

The amount of money that you need to deposit is $

$($Round to the nearest cent.$)$