PROBLEM # $1$: You are a local small investor in Houston, TX$.$ You opened a bank account today with a deposit of $$500\mathrm{.}00.$ Your plan is to make additional deposit of $$20$ every two months starting from the first month till the fifth month. At the seventh month you want to make a withdrawal of $$30$ every two months till the ${11}^{th}$ month. At the end of the year $($the ${12}^{th}$ month$),$ you will make a withdrawal of $$50\mathrm{.}00.$ Assuming that the bank gives you an interest rate of $2\%$ per month what is $($a$)$ the present worth of your investment in your transactions with the bank $($b$)$ what interest rate should the bank give you so that at the end of the year you have $$1,000\mathrm{.}00$ in your bank account? Draw the cash flow diagram. HINT: The withdrawals and deposits are made bimonthly, so it is better to convert the given interest rate per month compounded monthly to an effective interest rate per bimonthly compounded bimonthly. To find the interest rate that will give you $$1,000$ in your bank account at the end of the year, do trial and error of different interest rates and use a linear interpolation method to get the interest rate that will give you a future value of $$1000\mathrm{.}00$ at the end of the year. Or use the MS Excel function GOALSEEK to set up your Future Worth of your transactions to set a goal to seek for an interest rate that will make your future worth of your transactions at the end of the year to $$1,000\mathrm{.}00.$