A principal amount of $10,000 is invested in a continuously compounded account. After 15 years, the investment grows to $25,000. Find the annual interest rate. Round your answer to the nearest two decimal places in percentage form. Use the formula A = Pe^rt, where A is the balance (final amount), P is the principal (starting amount), e is the base of natural logarithms (≈2.71828), r is the interest rate expressed as a decimal, and t is the time in years.

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Identify values P, A, t: Identify the values for P, A, and t. P = 10,000 A = 25,000 t = 15Use formula A = Pe^(rt): Use the formula A = Pe^(rt). 25,000 = 10,000 * e^(15r)Divide both sides: Divide both sides by 10,000. 2.5 = e^(15r)Take natural logarithm: Take the natural logarithm (ln) of both sides. ln(2.5) = 15rSolve for r: Solve for r. r = ln(2.5) / 15Calculate ln(2.5): Calculate ln(2.5). ln(2.5) ≈ 0.9162907Divide by 15: Divide by 15. r ≈ 0.9162907 / 15 r ≈ 0.061086Convert r to percentage: Convert r to a percentage and round to two decimal places. r ≈ 0.061086 * 100 r ≈ 6.11%

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