$($Compound value$)$ Stanford Simmons, who recently sold his Porsche, placed $$11,000$ in a savings account paying annual compound interest of $6$ percent.

a$.$ Calculate the amount of money that will have accrued if he leaves the money in the bank for $2,5,$ and $15$ years.

b$.$ If he moves his money into an account that pays $8$ percent or one that pays $10$ percent, rework part a using these new interest rates.

c$.$ What conclusions can you draw about the relationship between interest rates, time, and future sums from the calculations you have completed in this problem?