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Part 1

Use

PMT equals StartFraction Upper P left parenthesis StartFraction r Over n EndFraction right parenthesis Over left bracket 1 minus left parenthesis 1 plus StartFraction r Over n EndFraction right parenthesis Superscript negative nt right bracket EndFraction

to determine the regular payment​ amount, rounded to the nearest dollar. Your credit card has a balance of

​$3600
 
and an annual interest rate of

17

​%. 

You decide to pay off the balance over

three
 
years. If there are no further purchases charged to the​ card,

a. How much must you pay each​ month?

b. How much total interest will you​ pay?

The given formula to calculate the monthly payment (PMT) on a loan or credit card balance is:

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

Where:

- $ P $ = Principal amount (in this case, the balance on the credit card) = 3600
- $ r $ = Annual interest rate (as a decimal) = 17% = 0.17
- $ n $ = Number of payments per year (monthly payments mean $ n = 12 $)
- $ t $ = Time to pay off the balance in years = 3

Now let's go step by step.

### Part a: How much must you pay each month?

We will substitute the values of $ P $, $ r $, $ n $, and $ t $ into the formula and solve for PMT.

\[
PMT = \frac{3600 \left( \frac{0.17}{12} \right)}{1 - \left(1 + \frac{0.17}{12}\right)^{-12 \times 3}}
\]

Let's calculate this.

### Part b: How much total interest will you pay?

To calculate the total interest paid, we first need to determine how much you will pay over the entire 3-year period:

\[
\text{Total Payments} = PMT \times (n \times t)
\]

Then subtract the original balance $ P $ from the total payments:

\[
\text{Total Interest} = \text{Total Payments} - P
\]

I'll calculate both parts now.### Part a: 
The monthly payment you must make to pay off the balance is approximately **$128**.

### Part b:
The total interest you will pay over the three years is approximately **$1,021**.

Would you like further clarification or details on any part of this?

Here are five related questions for further exploration:
1. How does changing the interest rate to 15% affect the monthly payment?
2. What would happen if the repayment period was extended to 5 years?
3. How is the formula different for biweekly payments instead of monthly?
4. What if additional charges were made to the card during the repayment period?
5. How can you calculate the balance remaining after 2 years of payments?

**Tip:** The longer you take to pay off a loan, the more you pay in interest! Always aim to reduce the repayment period when possible.

Use the formula PMT = \frac{P \left( \frac{r}{n} \right)}{1 - \left(1 + \frac{r}{n}\right)^{-nt}} to determine the regular payment amount, rounded to the nearest dollar. Your credit card has a balance of $3,600 and an annual interest rate of 17%. You decide to pay off the balance over three years. If there are no further purchases charged to the card, a. How much must you pay each month? b. How much total interest will you pay?

Learn how to calculate the monthly payment and total interest for a credit card balance of $3,600 at an annual interest rate of 17% over a 3-year period. This finance math problem uses the standard PMT formula to determine the regular payment amount and total interest. Ideal for students in Grades 10-12.

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