Questions: Assume you borrowed 100 on a credit card that charges an annual percentage rate of 20%, simple interest. How much would you owe after two weeks?

Solution Steps

To calculate the amount owed after two weeks with simple interest, we need to determine the interest accrued over that period. Simple interest is calculated using the formula \( I = P \times r \times t \), where \( P \) is the principal amount, \( r \) is the annual interest rate, and \( t \) is the time in years. Since the time given is in weeks, we need to convert it to years.

The time given is 2 weeks. To convert this to years, we use the conversion factor \( \frac{1}{52} \) since there are 52 weeks in a year. Thus, the time in years is: \[ t = \frac{2}{52} = \frac{1}{26} \approx 0.03846 \]

The simple interest \( I \) is calculated using the formula: \[ I = P \times r \times t \] where \( P = 100 \), \( r = 0.20 \), and \( t = 0.03846 \). Substituting these values, we get: \[ I = 100 \times 0.20 \times 0.03846 \approx 0.7692 \]

The total amount owed after two weeks is the sum of the principal and the interest: \[ \text{Total Amount} = P + I = 100 + 0.7692 \approx 100.77 \]

Final Answer