You just received a generous birthday present from your favorite Uncle $--$ $$1,000($partly a reward for the excellent grades you've been getting at Pace$).$ You plan on investing this cash and expect to earn a return of $9\%$ per year, compounded annually.

a$)$ How much will you have available in $10$ years?

b$)$ Your goal is to have $$3,500$ available in $10$ years. What rate of return $($rounded to $2$ decimal places$),$ compounded annually, would you have to earn to achieve your goal?

c$)$ The rate of return in part b$)$ above involves too much risk. If the maximum risk you're willing to accept involves a rate of return of $11\%$ per year, compounded annually, how long $($rounded to $2$ decimal places$)$ will it take to achieve your goal of $$3,500?$

d$)$ Suppose you could earn a rate of return of $15\%$ per year, compounded daily. How long would it take to achieve your goal now?