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 ​$4200 and an annual interest rate of 16​%. You decide to pay off the balance over five years. If there are no further purchases charged to the​ card,
a. How much must you pay each​ month?
b. How much total interest will you​ pay?
Question content area bottom
Part 1
a. The monthly payments are approximately ​$
  
enter your response here.  
​(Do not round until the final answer. Then round to the nearest dollar as​ needed.)

We are asked to determine the monthly payment to pay off a credit card balance of $4,200 over five years, with an annual interest rate of 16%. The formula for the payment amount (PMT) is given by:

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

where:
- $ P $ is the loan amount or balance ($4,200),
- $ r $ is the annual interest rate (16% or 0.16),
- $ n $ is the number of payments per year (12 for monthly payments),
- $ t $ is the number of years (5 years),
- $ nt $ is the total number of payments over the loan term (12 payments per year for 5 years, i.e., $ 12 \times 5 = 60 $ payments).

Now let's break down the calculation step by step.

### Step 1: Define the variables
- $ P = 4200 $
- $ r = 0.16 $
- $ n = 12 $
- $ t = 5 $
- $ nt = 60 $

### Step 2: Plug values into the formula

Now let's calculate the monthly payment using the formula.a. The monthly payments are approximately **$102**.

### Step 3: Calculate Total Interest Paid

To calculate the total interest paid, we first need to find the total amount paid over the five years and then subtract the initial balance.

\[
\text{Total Paid} = \text{PMT} \times nt
\]
\[
\text{Total Interest} = \text{Total Paid} - P
\]

Let's calculate the total interest now.b. The total interest paid over the five years is approximately **$1,928**.

If you have any questions about these calculations or would like more details, feel free to ask!

Here are 5 related questions to deepen your understanding:
1. How would the monthly payment change if the interest rate were lower, say 10%?
2. What happens to the total interest paid if you decide to pay off the balance in 3 years instead of 5?
3. How is the formula for PMT derived from the basic principles of interest and amortization?
4. What is the impact of making extra payments each month towards the credit card balance?
5. If there were an annual fee on the credit card, how would it affect your payment plan?

**Tip:** Always try to pay more than the minimum required amount on loans or credit cards to reduce the total interest paid over time.

Use PMT = (P(r/n)) / [1 - (1 + r/n)^(-nt)] to determine the regular payment​ amount, rounded to the nearest dollar. Your credit card has a balance of ​$4200 and an annual interest rate of 16​%. You decide to pay off the balance over five 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 monthly payments for a $4200 credit card balance with an annual interest rate of 16% over five years. This example uses the amortization formula to determine the monthly payment and total interest paid. Ideal for students in Grades 10-12 studying financial math.

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