Final answer:
To find the uniform end-of-year amount for 9 years that is equivalent to $8,000 at the end of year 9, we can use the formula for continuous compound interest. Plugging in the given values, the final amount is approximately $17,825.04.
Step-by-step explanation:
To find the uniform end-of-year amount for 9 years that is equivalent to $8,000 at the end of year 9, we need to use the formula for continuous compound interest. The formula is given by A = P * e^(rt), where A is the final amount, P is the initial principal, e is Euler's number approximately equal to 2.71828, r is the interest rate, and t is the time in years.
In this case, we have P = $8,000, r = 9% = 0.09, and t = 9 years. Plugging these values into the formula, we get:
A = $8,000 * e^(0.09*9)
Using a calculator or spreadsheet, we can find that e^(0.09*9) is approximately 2.71828^(0.81) = 2.22813. Multiplying this by $8,000 gives us the final answer:
A ≈ $8,000 * 2.22813 ≈ $17,825.04