Two receipts of $$1500$ each are desired at the EOYs $($end$-$of$-$years$)9$ and $10.$ To make these receipts possible, Four EOY annuity amounts will be deposited in a bank at EOYs $1,2,3$ and $4.$ If the bank$$s interest rate $($i$)$ is $12\%$ per year:

$($a$)$ Draw the cash flow diagram.

$($b$)$ Determine the value of A $($for the four EOY annuity amounts that will be deposited in a bank at EOYs $1,2,3$ and $4)$ that establishes equivalence in your cash$-$flow diagram.

$($c$)$ Determine the lump$-$sum value at the end of year $10$ of the completed cash$-$flow diagram based on your answer to part $($b$).$ keep attention to the signs of the cash flows $(+$ and $-)$ in this part of the question. Explain your answer to part $($c$).$