Q$1$: You just turned $20$ and decide that you would like to save up enough money so as to be able to withdraw $$100,000$ per year for $15$ years after you retire at age $65,$ with the first withdrawal starting on your $66$th birthday. How much money will you have to deposit each month into an account earning $5\%$ per year $($interest compounded monthly$),$ starting one month from today, to accomplish this goal?