The problem involves determining the monthly payment for a credit card balance of $4,000 with a 14% annual interest rate to be fully paid off in 4 years (48 months).

This requires using the formula for calculating fixed monthly payments for loans or credit balances:

$M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1}$

Where:

• $M$ = Monthly payment
• $P$ = Loan balance ($4,000)
• $r$ = Monthly interest rate (annual rate divided by 12, so $14\%/12 = 0.011667$)
• $n$ = Total number of payments (4 years × 12 months = 48)

Step 1: Define the values

• $P = 4,000$
• $r = 0.011667$
• $n = 48$

Step 2: Plug into the formula

Substitute these values into the formula to calculate $M$:

$M = \frac{4000 \cdot 0.011667 \cdot (1 + 0.011667)^{48}}{(1 + 0.011667)^{48} - 1}$

Let me compute this. Given values P = 4000 # Loan balance in dollars annual_rate = 0.14 # Annual interest rate r = annual_rate / 12 # Monthly interest rate n = 48 # Total number of payments (4 years * 12 months)

Monthly payment calculation

M = (P * r * (1 + r)**n) / ((1 + r)**n - 1) MThe monthly payment required to pay off the $4,000 credit card balance at a 14% annual interest rate in 4 years is approximately $109.31.

Would you like a detailed breakdown of the calculation or help with related concepts?

Related Questions

1. What happens if the interest rate is compounded differently, like daily or quarterly?
2. How does changing the repayment term (e.g., 5 years instead of 4) affect the monthly payment?
3. What is the total amount paid over the 4 years, including interest?
4. How much of the total payment goes toward interest versus principal repayment?
5. What would the monthly payment be if the balance was $5,000 instead of $4,000?

Tip:

When managing credit cards, aim to pay more than the minimum payment to reduce the total interest paid over time!