turkish govermnet is now planning to initiate a national budget savings program to construct "canal istanbul". Auction will be announced just after $5$ yeras from now. Consortiums, each made up of $3$ foreinngs and $2$ national construction companies willbe allowed to participate in the auction process. As the construction begins $,$ canal is expected to be complete in $4$ years. Currently the anual construction cost for everthing is $15$ billion tl$,$ but these cost are expected to increase by $5$ percent anually. after the auction process is complete the winning constrium will require that this amaount be paid at the start of the year. Public bank X will be responsible for all transactions and payments. Turkish teasury now has $7\mathrm{.}50$ billion tl in this bank account that pays $6$ percent annually. Govermnet must save annual deposite in this bank from its regular annual taxes. the govermnet must make $6$ equal annual deposite into this account, the $1$st deposite today and the $6$th on the day when construction begins.

a$)$in order for a succesful completion of canal istanbul, how large must each of the $6$ depoiste payments be$?$

b$)$ canal istanbul is expected to earn $10$ billion tl per year after the construction is complete. How much time it will take for the canal to pay itself back?