Final answer:
To calculate the amount owed after 6 months, use the formula for compound interest. You will owe approximately $549.90 after 6 months. To find out how long it will take to owe $700, solve the compound interest formula for time. It will take approximately 1.7725 years to owe $700.
Step-by-step explanation:
To calculate the amount owed after 6 months, we need to use the formula for compound interest: A = P*e^(rt), where A is the amount owed, P is the principal amount (initial amount), e is Euler's number (approximately 2.71828), r is the annual interest rate (0.19 in this case), and t is the time in years (6 months is 0.5).
- Substituting the values into the formula, we get A = 500*e^(0.19*0.5).
- Simplifying the expression, A = 500*e^(0.095).
- Using a scientific calculator or online tool, we find that e^(0.095) is approximately 1.0998.
- Multiplying 1.0998 by 500, we get A ≈ 549.9.
Therefore, after 6 months, you will owe approximately $549.90 on the credit card.
To find out how long it will take for you to owe $700, we need to solve the compound interest formula for time:
- Start with the equation A = P*e^(rt) and rearrange it to solve for t: t = (ln(A/P))/(r).
- Substituting the values, we have t = (ln(700/500))/(0.19).
- Using a logarithmic calculator or online tool, we find that ln(700/500) is approximately 0.33647.
- Dividing 0.33647 by 0.19, we get t ≈ 1.7725 years.
Therefore, it will take approximately 1.7725 years (or approximately 1 year and 9 months) for you to owe $700 on the credit card.