Final answer:
To find the amount after 8 years with continuous compounding, you can use the formula A = Pe^(rt), where A is the final amount, P is the initial principal, e is the base of natural logarithms (approximately 2.71828), r is the annual interest rate as a decimal, and t is the number of years. In this case, the initial principal is $2000, the annual interest rate is 8%, and the number of years is 8. The final amount after 8 years is approximately $4355.62.
Step-by-step explanation:
To find the amount after 8 years with continuous compounding, you can use the formula A = Pe^(rt), where A is the final amount, P is the initial principal, e is the base of natural logarithms (approximately 2.71828), r is the annual interest rate as a decimal, and t is the number of years.
In this case, the initial principal is $2000, the annual interest rate is 8%, and the number of years is 8. Plugging these values into the formula, you get:
A = 2000 * e^(0.08 * 8)
Calculating this, the final amount after 8 years is approximately $4355.62.