Question 62159
<b>A bank credit card charges interest at the rate of 21% per year, compounded monthly.  If a senior in college chares her last tuition bill of $1,500 and intends to pay it in one year, what will she have to pay.  </b>

21% per year interest = 21/12 = 1 3/4% per month = .0175.

If the student charges $1500 then after one month she'll owe 1500 (balance) + .0175*1500 (interest). We can write the balance after 1 month as {{{1500*1.0175}}}.

After 2 months she'll owe 1500*1.0175 times another 1.0175 on the balance after the first month plus its interest. The balance after 2 months = {{{1500*1.0175^2}}}.

Repeating the pattern, after 12 months her balance = {{{1500*1.0175^12}}}.

Use a calculator and you get $1847.16 as the balance after 12 months.