You invest $5,000 in a savings account that offers an annual interest rate of 6%, compounded annually. How long will it take for your investment to grow to $8,000? 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 = $5,000 A = $8,000 r = 0.06 n = 1Use formula and solve: Use the formula A = P(1 + (r)/(n))^nt and solve for t. 8,000 = 5,000(1 + 0.06/1)^(1*t) 8,000 = 5,000(1.06)^tDivide to isolate term: Divide both sides by 5,000 to isolate the exponential term. 8,000 / 5,000 = (1.06)^t 1.6 = (1.06)^tTake natural logarithm: Take the natural logarithm (ln) of both sides to solve for t. ln(1.6) = ln((1.06)^t) ln(1.6) = t * ln(1.06)Divide to isolate t: Divide both sides by ln(1.06) to isolate t. t = ln(1.6) / ln(1.06)Calculate value of t: Calculate the value of t. t = ln(1.6) / ln(1.06) t ≈ 0.470 / 0.058 t ≈ 8.10

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