You just bought a new tablet computer for $\$500$ including tax. There are no required payments for six months, but the company does charge $30\%$ annual interest, compounded monthly, on any unpaid balance.

1. What is the monthly interest rate?

   Hint (a):

   Annual is yearly, so $30\%$ per year is what percent each month?

   Answer (a):

   $2.5\%$

2. Write an equation that models the cost of your tablet each month if you make no payments.

   Answer (b):

   $t\left(n\right)=a\left(1+r\right)^{n}$

   Substitution yields:
   $t(n)=500(1+0.025)^n$where $n$ represents time in months.

3. If you do not make any payments for six months, how much will you owe for your new tablet?

   Hint (c):

   Use the equation in part (b).

   Answer (c):

   $\$579.85$

4. What is the effective annual rate of interest if you do not make any payments for a year? (Hint: Because the interest is compounded monthly, the effective, or actual annual rate is higher than $30\%$.)

   Hint (d):

   Using the equation from part (b), how much money in interest would you have paid for twelve months? What percentage of $\$500$ is this?