Suppose you deposit $\$50$ in Piggy Bank, which pays $5.5\%$ annual interest. How much money will be in your account:

1. After $6$ months if the interest is compounded twice a year?

   Step (a):

   $50\left(1+\frac{0.055}{2}\right)^1=\underline{\ \ \ \ \ \ }$

2. After $1$ year if the interest is compounded twice a year?

   Hint (b):

   Refer to hint in part (a).

3. After $1$ year if the interest is compounded monthly?

   Hint (c):

   $\text{investment }\left(1+\frac{\text{rate}}{\text{times compounded}}\right)^{12}=\underline{\ \ \ \ \ \ }$

4. After $2$ years if the interest is compounded monthly?

   Hint (d):

   Refer to hint in part (c).

5. After $2$ years if the interest is compounded daily?

   Hint (e):

   Refer to hint in part (c).

6. Why was your answer to part (e) larger than your answer to part (d)?

   Hint (f):

   Which Piggy Bank plan would you choose?