To calculate the final loan amount of a credit card loan with compound interest, you can use the formula for compound interest:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial loan amount).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the number of years the money is invested or borrowed.
For your calculation:
- \( P = 500 \) (the principal amount)
- \( r = 0.16 \) (16% as a decimal)
- \( n = 12 \) (interest is compounded monthly)
- \( t = 1 \) (for 1 year)
Plugging in the values:
\[ A = 500 \left(1 + \frac{0.16}{12}\right)^{12 \times 1} \] \[ A = 500 \left(1 + 0.0133333\right)^{12} \] \[ A = 500 \left(1.0133333\right)^{12} \]
Calculating \( (1 + 0.0133333)^{12} \):
\[ A = 500 \left(1.1734\right) \] (approximately)
\[ A \approx 586.70 \]
Therefore, the closest option to the final amount calculated is $586.14.
Correct answer: $586.14.