The following table shows the expenses and payments for 2 months on a credit card account with an initial balance of $617. Assume that the interest rate is 1% per month (12% APR) and that the interest for a given month is charged on the balance from the previous month.
 
This means the amount owed in interest each month is the output of a function,  f(x) , that uses the input of the previous month's balance,  x .
f(x)=0.01∗x 
 
The new month's balance is the output of a function,  g(x,p,e,a) , that use the following inputs:
x , the previous month's balance
p , the payment
e , the expenses charged on credit for the month
a , the amount owed in interest
g(x,p,e,a)=x−p+e+a 
 
Use the two functions to fill in the table below. For each question, round to the nearest penny and don't use commas or dollar signs.
Month	Payment	Expenses	Interest	Balance
0	-	-	-	$617
1	$141	$101	$   	$  
2	$56	$39	$  	$  


We have two functions:

1. **Interest calculation:**  
   \[
   f(x) = 0.01 \cdot x
   \]
   This gives the interest based on the previous month's balance.

2. **Balance update calculation:**  
   \[
   g(x, p, e, a) = x - p + e + a
   \]
   This calculates the new balance based on the previous month's balance $x$, the payment $p$, the expenses $e$, and the interest $a$.

### Month 0
- **Initial balance (Month 0):** $617
- Since no payments or expenses are made in Month 0, no calculation is needed.

### Month 1
- **Previous balance (Month 0):** $617
- **Payment for Month 1:** $141
- **Expenses for Month 1:** $101

#### Step 1: Calculate the interest for Month 1 using $f(x)$:
\[
f(617) = 0.01 \times 617 = 6.17
\]
Interest = **$6.17**

#### Step 2: Calculate the new balance for Month 1 using $g(x, p, e, a)$:
\[
g(617, 141, 101, 6.17) = 617 - 141 + 101 + 6.17 = 583.17
\]
Balance at the end of Month 1 = **$583.17**

### Month 2
- **Previous balance (Month 1):** $583.17
- **Payment for Month 2:** $56
- **Expenses for Month 2:** $39

#### Step 1: Calculate the interest for Month 2 using $f(x)$:
\[
f(583.17) = 0.01 \times 583.17 = 5.83
\]
Interest = **$5.83**

#### Step 2: Calculate the new balance for Month 2 using $g(x, p, e, a)$:
\[
g(583.17, 56, 39, 5.83) = 583.17 - 56 + 39 + 5.83 = 571.00
\]
Balance at the end of Month 2 = **$571.00**

### Final Table

| Month | Payment | Expenses | Interest | Balance  |
|-------|---------|----------|----------|----------|
| 0     | -       | -        | -        | 617.00   |
| 1     | 141.00  | 101.00   | 6.17     | 583.17   |
| 2     | 56.00   | 39.00    | 5.83     | 571.00   |

Would you like further clarification or details?

#### Related Questions
1. How would the balance change if the interest rate increased to 2% per month?
2. What would happen if the payments were reduced to half of their current amounts?
3. How much total interest will accumulate over 12 months if the expenses and payments remain consistent?
4. What is the total amount paid in payments by the end of Month 2?
5. How can you calculate the total interest paid over the 2 months?

#### Tip
To minimize interest charges on a credit card, try to pay off the balance in full each month.

The following table shows the expenses and payments for 2 months on a credit card account with an initial balance of $617. Assume that the interest rate is 1% per month (12% APR) and that the interest for a given month is charged on the balance from the previous month.
This means the amount owed in interest each month is the output of a function, f(x), that uses the input of the previous month's balance, x. f(x) = 0.01 * x
The new month's balance is the output of a function, g(x,p,e,a), that uses the following inputs: x, the previous month's balance; p, the payment; e, the expenses charged on credit for the month; a, the amount owed in interest.
Use the two functions to fill in the table below. For each question, round to the nearest penny and don't use commas or dollar signs.

Solve a credit card interest and balance calculation problem using linear functions. Given an initial balance of $617, a 1% monthly interest rate, and various payments and expenses, learn how to compute interest and update the balance for two months. Suitable for students in Grades 9-11.

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