You deposit $15,000 into a savings account with an annual interest rate of 5%, compounded annually. How long will it take for the account balance to grow to $25,000? 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

You deposit $15,000 into a savings account with an annual interest rate of 5%, compounded annually. How long will it take for the account balance to grow to $25,000? 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.

Bytelearn · Accepted Answer

Identify values: Identify the values of P, r, n, and A. P = $15,000 r = 0.05 n = 1 A = $25,000Substitute values in formula: Substitute P = 15000, r = 0.05, n = 1, and A = 25000 in the formula. 25000 = 15000(1 + (0.05)/(1))^(1 * t) 25000 = 15000(1.05)^tDivide to isolate: Divide both sides by 15000 to isolate (1.05)^t. 25000 / 15000 = (1.05)^t 1.6667 = (1.05)^tTake natural logarithm: Take the natural logarithm (ln) of both sides to solve for t. ln(1.6667) = ln((1.05)^t) ln(1.6667) = t * ln(1.05)Divide to solve for t: Divide both sides by ln(1.05) to solve for t. t = ln(1.6667) / ln(1.05) t ≈ 0.5108 / 0.04879 t ≈ 10.47

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