Your brother has offered to give you $$$$125,$ starting next$$ 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 $5\mathrm{.}7\%$ 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.$)$