Final answer:
Jackson's credit card debt, with a 2.8% annual interest rate compounded continuously, will be calculated using the formula A = Pe^(rt). By substituting Jackson's debt amount and the given interest rate, the future debt can be found after performing the appropriate mathematical operations and rounding to the nearest cent.
Step-by-step explanation:
To calculate how much Jackson will owe on his credit card debt after 5 years with continuous compounding at an annual interest rate of 2.8%, we can use the formula for continuous compounding, which is A = Pert, where P is the principal amount (initial loan), r is the annual interest rate in decimal form, t is the time in years, and e is the natural logarithm base (approximately equal to 2.71828).
First, we convert the annual interest rate from a percentage to a decimal by dividing by 100: r = 2.8% / 100 = 0.028.
Next, we insert the values we know into the formula: A = 9000e(0.028 × 5).
After performing the calculations, we get A = 9000e0.14. Evaluating e to the power of 0.14 and then multiplying by 9000 gives us the final amount Jackson owes. It is important to round the final answer to the nearest cent after all calculations have been completed to get the most accurate amount due.
Assuming no payments are made for 5 years, the continuous compounding will result in Jackson owing more than the initial $9,000 due to the interest accruing continuously at the provided interest rate.