  ### Home > INT2 > Chapter 5 > Lesson 5.1.3 > Problem5-36

5-36.

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?

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

$2.5\%$

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

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

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?

Use the equation in part (b).

$\579.85$

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 $30\%$.)

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