A college fund of $10,000 is set up with an annual interest rate of 4%, compounded annually. How many years will it take for the fund to reach $15,000? Use the formula A = P(1 + (r)/(n))^nt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years. Round your answer to the nearest hundredth.

Question

A college fund of $10,000 is set up with an annual interest rate of 4%, compounded annually. How many years will it take for the fund to reach $15,000?  Use the formula A = P(1 + (r)/(n))^nt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years. Round your answer to the nearest hundredth.

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Identify Values: Identify the values of P, r, n, and A. P = 10000 r = 0.04 n = 1 A = 15000Use Formula and Solve: Use the formula A = P(1 + (r)/(n))^nt and solve for t. 15000 = 10000(1 + 0.04)^tDivide and Simplify: Divide both sides by 10000. 1.5 = (1.04)^tTake Natural Logarithm: Take the natural logarithm (ln) of both sides to solve for t. ln(1.5) = ln((1.04)^t)Apply Logarithm Property: Use the property of logarithms: ln(a^b) = b*ln(a). ln(1.5) = t * ln(1.04)Isolate t: Divide both sides by ln(1.04) to isolate t. t = ln(1.5) / ln(1.04)Calculate t: Calculate the value of t. t ≈ ln(1.5) / ln(1.04) t ≈ 0.405465 / 0.039221 t ≈ 10.34

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