(Please include a cash flow diagram) A teacher is interested to open investments account at an interest rate of 12% compounded semiannually. The scheme allows for the investor to withdraw a certain annuity for the first 3 years. This annuity increases by a factor of 1.5 for the next three years and becomes twice the initial annuity thereafter. If he wants to withdraw a perpetuity of $65,000, how much should he deposit?