Rachel is purchasing a new camera that costs $2800$⁢2800. Rachel uses a credit card that has an APR of 19.33%19.33%. How much will she pay in total to pay off the purchase if she makes monthly payments of $80$⁢80? Round the number of monthly payments up to the nearest whole number. Round your final answer to the nearest whole number, if necessary.

To determine how much Rachel will pay in total to pay off her $2,800 purchase with an APR of 19.33%, we need to calculate the total payments using the formula for monthly payments with interest.

### Step 1: Determine the monthly interest rate.
The APR (Annual Percentage Rate) is 19.33%, so the monthly interest rate is:

\[
r = \frac{19.33\%}{12} = \frac{19.33}{100 \times 12} = 0.01611 \text{ (or 1.611% per month)}
\]

### Step 2: Use the formula for the total number of payments.
The formula for the total number of payments, $ N $, to pay off a loan is:

\[
N = \frac{\ln\left(\frac{P}{P - M \times r}\right)}{\ln(1 + r)}
\]

Where:
- $ P $ is the principal amount ($2,800),
- $ M $ is the monthly payment ($80),
- $ r $ is the monthly interest rate (0.01611).

We will calculate $ N $ using this formula.

### Step 3: Calculate the total amount paid.

Let me calculate the exact number of months and the total amount paid.It seems that the calculated result suggests only 1 payment, which is incorrect based on the context. I will revise the calculation approach to ensure accuracy. Let me try again.Rachel will need **52 months** to pay off the camera. The total amount she will pay, including interest, is **$4,160**.

Would you like more details or have any further questions?

Here are 5 related questions to expand on the topic:
1. How would Rachel's total payment change if she made larger monthly payments?
2. What happens to the number of payments if the interest rate increases?
3. How much interest will Rachel pay over the entire period?
4. How can Rachel minimize the interest she pays on her credit card balance?
5. How would a different loan term affect the total cost?

**Tip:** Making larger payments reduces the total interest paid over time!

Rachel is purchasing a new camera that costs $2800. Rachel uses a credit card that has an APR of 19.33%. How much will she pay in total to pay off the purchase if she makes monthly payments of $80? Round the number of monthly payments up to the nearest whole number. Round your final answer to the nearest whole number, if necessary.

Learn how to calculate the total payment for a $2,800 purchase with an APR of 19.33% and monthly payments of $80. This example covers the calculation of monthly interest rates and the formula for the total number of payments. Suitable for students in Grades 10-12.

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