Problem if $3$: You started an investment today by depositing $$100K$ in a bank that pays $10\%$ interest rate per year. You later make additional deposit of $$10K$ overy year for the next $10$ years $($that is from year $1$ to year $10$ you deposit $$10K$ every year$).$ You also made withdrawals of $$5K$ each in the first, second, and third year. In the third and $10$ year you made additional withdrawals of $$3K$ each and deposited additional $$6K$ in the finth year.

$($a$)$ Draw the cash flow diagram for all the above transactions.

$($b$)$ Calculate the present value of the transactions.

$($C$)$ Calculate the future value of the transactions.