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.