Final answer:
Larry's debt grows over time due to the compounded interest charged by the credit-card company. After 1 year, Larry's debt will grow to $324.26.
Step-by-step explanation:
Larry's debt grows over time due to the compounded interest charged by the credit-card company. The interest rate is 18% per year and is compounded monthly. To calculate the growth of Larry's debt, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the future value, P is the principal (initial debt), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, Larry's initial debt is $285, the annual interest rate is 18%, the number of times interest is compounded per year is 12 (monthly), and let's assume he will carry the debt for 1 year.
Using the formula, A = 285(1 + 0.18/12)^(12*1), we can calculate the future value of Larry's debt after 1 year. Plugging in the values, we get A = 285(1 + 0.015)^(12) = 285(1.015)^(12) = 324.26. Therefore, Larry's debt will grow to $324.26 after 1 year.