To calculate the balance of the credit card after three months, we can use the formula for compound interest. The monthly interest rate is determined by dividing the annual percentage rate (APR) by 12.
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Calculate the monthly interest rate: \[ \text{Monthly Interest Rate} = \frac{12.75%}{12} = 1.0625% = 0.010625 \]
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Use the compound interest formula: The formula to calculate the future balance with compounded interest is: \[ A = P(1 + r)^n \] where:
- \(A\) is the amount of money accumulated after n months, including interest.
- \(P\) is the principal amount (the initial balance).
- \(r\) is the monthly interest rate (as a decimal).
- \(n\) is the number of months the money is invested or borrowed.
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Plug in the values:
- \(P = 3168\)
- \(r = 0.010625\)
- \(n = 3\)
\[ A = 3168(1 + 0.010625)^3 \]
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Calculate: \[ A = 3168(1.010625)^3 \] \[ A = 3168 \times 1.032161 \] \[ A \approx 3273.94 \]
Therefore, the balance after three months is approximately $3,273.94.
Looking at the provided responses, none of them match our calculated balance directly. The closest approximation in the responses is $3,270.06; however, this should be verified with a precise calculation or rounding method.
So, given the options provided, the best choice would be:
$3,270.06
1 answer