PROBLEM # $3.$ You deposited $$100$ in to your bank account today and two years from now you will withdraw $$10$ per year for the next three years. Thereafter you will deposit additional $$25$ five years from now and withdraw additional $$10$ a year after this deposit. $($a$)$ Calculate how much you will have in your bank account seven years from now if you want to close your bank account. $($Hint: Calculate the future worth of all your transactions in the $7^{th}$ year.$)($b$)$ Calculate the present worth of all your transactions. Assume that all transactions attract an interest rate of $1\%$ per month compounded quarterly. You must draw the cash flow diagram. Hint translate to effective interest rate per year.