You just received a generous birthday present from your favorite Uncle $--$ $$200($partly a reward for the excellent grades you've been getting at Pace$).$ You plan on investing this cash and expect to earn a return of $7\%$ per year, compounded annually.

a$)$ How much $($rounded to the nearest penny$)$ will your investment grow to in $10$ years?

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

c$)$ The rate of return in part b$)$ above involves too much risk for you. If the maximum risk you're willing to accept involves a rate of return of $8\%$ per year, compounded annually, how many years will it take to achieve your goal of $$500($round your answer to two decimal places$)?$

d$)$ Suppose you could earn a rate of return of $8\%$ per year, compounded daily. How long would it take to achieve your goal $($in years$)$ now $($round your answer to two decimal places$)?$