Credit Card Interest 2694Ac

1. **State the problem:** A customer buys a computer for $1800$ using a store credit card with an APR of $17.99\%$. They pay $125$ per month until the balance is paid off. We need to find the total interest paid. 2. **Understand the formula and rules:** The APR (Annual Percentage Rate) is $17.99\%$, which means the interest is compounded monthly at a rate of $\frac{17.99}{12} \% = 1.4992\%$ per month approximately. The monthly interest rate $i = \frac{17.99}{100 \times 12} = 0.014992$. The monthly payment is $P = 125$. The initial loan amount (principal) is $L = 1800$. 3. **Calculate the number of months to pay off the loan:** The formula for the number of payments $n$ to pay off a loan with fixed monthly payments is: $$ n = \frac{\log\left(\frac{P}{P - iL}\right)}{\log(1 + i)} $$ Substitute values: $$ n = \frac{\log\left(\frac{125}{125 - 0.014992 \times 1800}\right)}{\log(1 + 0.014992)} = \frac{\log\left(\frac{125}{125 - 26.986}\right)}{\log(1.014992)} = \frac{\log\left(\frac{125}{98.014}\right)}{\log(1.014992)} $$ Calculate numerator: $$ \log\left(1.275\right) \approx 0.1063 $$ Calculate denominator: $$ \log(1.014992) \approx 0.00646 $$ So, $$ n = \frac{0.1063}{0.00646} \approx 16.46 \text{ months} $$ Since payments are monthly, the customer will make $17$ payments. 4. **Calculate total amount paid:** $$ \text{Total paid} = 17 \times 125 = 2125 $$ 5. **Calculate total interest paid:** $$ \text{Interest} = \text{Total paid} - \text{Principal} = 2125 - 1800 = 325 $$ 6. **Adjust for partial last payment:** Since $16.46$ months is not a full payment, the last payment will be less than $125$. The exact interest is slightly less than $325$. 7. **Conclusion:** The closest answer choice to the calculated interest is $295.01$. **Final answer:** $295.01$