Omar was $8$ years old when he received $$25{,}000$ dollars from his grandmother’s will. His father invested it for him in a fund that earned $6\%$ annual interest compounded quarterly. He was hoping to see the investment double by the time Omar was ready for college. Another fund offered the same interest rate but the interest would compound continuously. This second fund was a little riskier, however.

1. Write an equation to represent each situation.

   Answer (a):

   $2 = (1.015)^{4t}, 2 = e^{0.06t}$

2. Which method of compounding the interest will double his money faster?

   Hint (b):

   Solve both equations for $t$.

3. Is the difference in doubling time worth the extra risk?

   Hint (c):

   What is the difference in doubling time?