You have \( \$ 5,000 \) on a credit card that charges a \( 18 \% \) interest rate. If you want to pay off the credit card in 3 years, how much will you need to pay each month (assuming you don't charge anything new to the card)?

To pay off a credit card balance of \( \$5,000 \) at an \( 18\% \) annual interest rate over \( 3 \) years, you can use the formula for an amortizing loan: \[ M = P \frac{r(1+r)^n}{(1+r)^n - 1} \] where \( M \) is the monthly payment, \( P \) is the principal amount (\$5,000), \( r \) is the monthly interest rate (annual rate / 12), and \( n \) is the number of payments (months). First, calculate the monthly interest rate: \( r = \frac{0.18}{12} \approx 0.015 \). The total number of payments over \( 3 \) years is \( n = 3 \times 12 = 36 \). Plugging these into the formula, you get: \[ M = 5000 \frac{0.015(1+0.015)^{36}}{(1+0.015)^{36} - 1} \] Calculating this gives you approximately \( M \approx \$ 176.68 \). Thus, you would need to pay about \( \$176.68 \) each month to pay off the credit card debt in three years. To put it all in perspective, it's worth noting that credit cards can be a double-edged sword. On one hand, they offer convenience and can help you build your credit history. On the other hand, high-interest rates like 18% can turn manageable expenses into hefty financial burdens if not paid off swiftly. So, always be cautious with that shiny plastic!