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

Question

UpStudy AI · Accepted Answer

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

Real Tutor Solution

Answer

Solution

Mind Expander

Related Questions

Latest Arithmetic Questions