You invested $4,000 in a savings account, and after 9 years, the balance grew to $6,561.60. The interest is compounded annually. What is the annual interest rate? 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 tenth.

Question

You invested $4,000 in a savings account, and after 9 years, the balance grew to $6,561.60. The interest is compounded annually. What is the annual interest rate? 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 tenth.

Bytelearn · Accepted Answer

Identify Given Values: Identify the given values. A = $6,561.60, P = $4,000, t = 9 years, n = 1 (compounded annually)Use Formula: Use the formula A = P(1 + (r)/(n))^nt. 6,561.60 = 4,000(1 + r)^9Isolate (1 + r)^9: Divide both sides by 4,000 to isolate (1 + r)^9. (6,561.60) / (4,000) = (1 + r)^9 1.6404 = (1 + r)^9Solve for (1 + r): Take the 9th root of both sides to solve for (1 + r). (1.6404)^(1/9) = 1 + r 1.056 = 1 + rSolve for r: Subtract 1 from both sides to solve for r. 1.056 - 1 = r r = 0.056Convert to Percentage: Convert r to a percentage by multiplying by 100. 0.056 * 100 = 5.6%

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