Pregunta
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Travis Thompson uses his credit card to obtain a cash advance of \( \$ 600 \) to pay for his textbooks in medical school. The interest rate charged for the loan is \( 0.04926 \% \) per day. Travis repays the money plus the interest after 20 days. a) Determine the interest charged for the cash advance. b) When he repaid the loan, how much did he pay the credit card company? Interest charged \( \approx \$ \square \) (Round to the nearest tent.)

Ask by Curry Weston. in the United States
Dec 03,2024

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a) The interest charged for the cash advance is approximately $5.91. b) Travis paid the credit card company approximately $605.91.

Solución

Given: - Travis Thompson obtained a cash advance of $600. - The interest rate charged for the loan is 0.04926% per day. - Travis repays the money plus the interest after 20 days. a) To determine the interest charged for the cash advance, we can use the formula for simple interest: \[ I = P \times r \times t \] where: - \( I \) is the interest charged, - \( P \) is the principal amount (cash advance amount), - \( r \) is the interest rate per day, - \( t \) is the time in days. Substitute the given values into the formula: - \( P = \$600 \) - \( r = 0.04926\% = 0.0004926 \) (convert percentage to decimal) - \( t = 20 \) days Calculate the interest charged: \[ I = 600 \times 0.0004926 \times 20 \] b) To find out how much Travis paid the credit card company when he repaid the loan, we need to add the principal amount and the interest charged. Let's calculate the interest charged first. Calculate the value by following steps: - step0: Calculate: \(600\times 0.0004926\times 20\) - step1: Multiply the terms: \(0.29556\times 20\) - step2: Multiply the numbers: \(5.9112\) a) The interest charged for the cash advance is approximately $5.91. Now, let's calculate how much Travis paid the credit card company when he repaid the loan. Calculate the value by following steps: - step0: Calculate: \(600+5.9112\) - step1: Add the numbers: \(605.9112\) b) When Travis repaid the loan, he paid the credit card company approximately $605.91.

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Beyond the Answer

To determine the interest charged for the cash advance, we can use the formula for simple interest: \[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \] where the principal is \( \$ 600 \), the rate is \( 0.04926\% \) per day (which is \( 0.0004926 \) in decimal), and the time is 20 days. Calculating the interest: \[ \text{Interest} = 600 \times 0.0004926 \times 20 \approx 5.9112 \] Rounding to the nearest tent: **Interest charged \( \approx \$ 5.9 \)** To find out how much Travis paid back in total, we simply add the principal to the interest: \[ \text{Total Payment} = \text{Principal} + \text{Interest} = 600 + 5.9112 \approx 605.9112 \] Rounding to the nearest tent, Travis paid back: **Total amount paid \( \approx \$ 605.9 \)**

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