You have a credit card that has a balance of $$ \$ 8930 $$ at an APR of $$ 16.49 \% $$. You plan to pay $$ \$ 400 $$ each month in an effort to clear the debt quickly. How many months will it take you to pay off the balance? Formulas Answer How to enter vour

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To determine how many months it will take to pay off your credit card balance of **\$8,930** with an Annual Percentage Rate (APR) of **16.49%** by making monthly payments of **\$400**, you can use the following formula:

### **Formula**

$$
n = \frac{-\ln\left(1 - \frac{r \times P}{A}\right)}{\ln(1 + r)}
$$

**Where:**
- $$ n $$ = Number of months to pay off the debt
- $$ P $$ = Principal amount (\$8,930)
- $$ A $$ = Monthly payment (\$400)
- $$ r $$ = Monthly interest rate (APR divided by 12)

### **Step-by-Step Calculation**

1. **Convert APR to Monthly Interest Rate:**
   
   $$
   r = \frac{16.49\%}{12} = 1.37417\% \text{ per month} = 0.0137417 \text{ (in decimal)}
   $$

2. **Plug Values into the Formula:**
   
   $$
   n = \frac{-\ln\left(1 - \frac{0.0137417 \times 8930}{400}\right)}{\ln(1 + 0.0137417)}
   $$

3. **Calculate the Numerator Inside the Logarithm:**
   
   $$
   \frac{0.0137417 \times 8930}{400} = \frac{122.72}{400} = 0.3068
   $$
   
   $$
   1 - 0.3068 = 0.6932
   $$

4. **Compute the Natural Logarithms:**
   
   $$
   \ln(0.6932) \approx -0.3662
   $$
   
   $$
   \ln(1 + 0.0137417) \approx 0.01364
   $$

5. **Calculate $$ n $$:**
   
   $$
   n = \frac{-(-0.3662)}{0.01364} \approx \frac{0.3662}{0.01364} \approx 26.83 \text{ months}
   $$

### **Final Answer**

It will take approximately **27 months** to pay off your credit card balance of \$8,930 by making monthly payments of \$400 at an APR of 16.49%.

### **Summary Table**

| **Parameter**        | **Value**         |
|----------------------|-------------------|
| Principal ($$ P $$)          | \$8,930           |
| Annual Interest Rate (APR)   | 16.49%            |
| Monthly Interest Rate ($$ r $$) | 1.37417% (0.0137417) |
| Monthly Payment ($$ A $$)    | \$400             |
| Number of Months ($$ n $$)   | ~27 months        |

### **Note**

- **Rounding:** Since you cannot make a fraction of a payment, you should plan for **27 full monthly payments** to completely pay off the debt.
- **Interest Accumulation:** This calculation assumes that the interest is compounded monthly and that each payment is made on time every month.
It will take approximately 27 months to pay off the \$8,930 credit card balance with a 16.49% APR by making \$400 monthly payments.

You have a credit card that has a balance of \( \$ 8930 \) at an APR of \( 16.49 \% \). You plan to pay \( \$ 400 \) each month in an effort to clear the debt quickly. How many months will it take you to pay off the balance? Formulas Answer How to enter vour

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