Suppose that you owe $4,000 on your credit card, the company charges 1.3% interest per month, and you just let the balance ride. Over the period of two years, rounded to the nearest penny, you will pay $_____ in interest.


To find out how much interest you will pay over two years, we can use the formula for compound interest, since the interest is applied monthly.

The formula for compound interest is:

\[
A = P \times \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ A $ is the amount of money accumulated after $ n $ periods (including interest).
- $ P $ is the principal amount (the initial amount of money).
- $ r $ is the annual interest rate (as a decimal).
- $ n $ is the number of times that interest is compounded per unit $ t $.
- $ t $ is the time the money is invested or borrowed for, in years.

In this case:
- $ P = 4000 $ dollars
- $ r = 0.013 \times 12 = 0.156 $ (since 1.3% interest per month equals 15.6% annual interest)
- $ n = 12 $ (since the interest is compounded monthly)
- $ t = 2 $ years

First, we'll calculate the total amount $ A $, and then we'll find the interest by subtracting the principal $ P $ from $ A $.

Let's compute this.Over the period of two years, you will pay $1,453.64 in interest, rounded to the nearest penny.

Would you like more details on how this was calculated, or do you have any questions?

Here are five related questions to consider:
1. What would the interest be if the interest rate was increased to 2% per month?
2. How would the total interest change if you made a payment each month?
3. What is the total amount you will owe after two years, including interest?
4. How long would it take to double your debt at this interest rate without making payments?
5. What is the effect of paying only the minimum balance each month on the total interest paid?

**Tip:** Making regular payments, even if small, can significantly reduce the amount of interest you pay over time.

Suppose that you owe $4,000 on your credit card, the company charges 1.3% interest per month, and you just let the balance ride. Over the period of two years, rounded to the nearest penny, you will pay $_____ in interest.

Discover how to calculate the interest paid on a $4,000 credit card balance with a 1.3% monthly interest rate over two years. Using the compound interest formula, this solution walks through step-by-step calculations and explains key concepts such as exponential growth and monthly compounding. Suitable for Grades 9-12.

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