You have $3500 on a credit card that charges a 22.54% Annual Percentage Rate. If you want to pay off the credit card in 5 years, how much will you need to pay each month (assuming you don't charge anything new to the card)?
What will your monthly payment be?
$

How much will you have paid to the credit card company over the 5 years?
$

How much total interest did you pay?
$


To solve this problem, we'll use the formula for calculating the monthly payment on a loan or credit card balance, which is derived from the annuity formula:

\[
M = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1}
\]

where:
- $ M $ is the monthly payment.
- $ P $ is the principal amount (initial balance), which is $3500.
- $ r $ is the monthly interest rate, calculated as the annual interest rate divided by 12.
- $ n $ is the total number of payments (months), which is the number of years multiplied by 12.

### 1. Calculating the Monthly Payment:

1. **Annual Percentage Rate (APR)** = 22.54%
2. **Monthly Interest Rate (r)** = 22.54% / 12 = 0.02254 / 12
3. **Number of Payments (n)** = 5 years × 12 months/year = 60 months

We'll plug these values into the formula to find the monthly payment $ M $.

### 2. Calculating the Total Amount Paid:

The total amount paid over the 5 years is the monthly payment multiplied by the number of payments.

\[
\text{Total Paid} = M \times n
\]

### 3. Calculating the Total Interest Paid:

The total interest paid is the difference between the total amount paid and the principal.

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

Let's calculate these values step-by-step.### Results:
1. **Monthly Payment:** $97.74
2. **Total Paid Over 5 Years:** $5864.63
3. **Total Interest Paid:** $2364.63

Would you like more details on any of these calculations, or do you have any further questions?

Here are 5 related questions you might find useful:
1. How would the monthly payment change if the interest rate was lower?
2. What happens to the monthly payment if the repayment period is shortened to 3 years?
3. How does the total interest paid compare with a lower principal amount?
4. What impact does making an extra payment each month have on the total interest paid?
5. How is the formula for monthly payments derived?

**Tip:** Making even small additional payments each month can significantly reduce the total interest paid over the life of a loan.

You have $3500 on a credit card that charges a 22.54% Annual Percentage Rate. If you want to pay off the credit card in 5 years, how much will you need to pay each month (assuming you don't charge anything new to the card)? What will your monthly payment be? How much will you have paid to the credit card company over the 5 years? How much total interest did you pay?

Calculate the monthly payment required to pay off a $3500 credit card debt at 22.54% APR in 5 years. This solution includes step-by-step calculations for the monthly payment, total amount paid, and total interest paid, making it ideal for anyone managing personal finance or learning about loan amortization.

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