You invested $7,500 in a savings account, and after 8 years, the balance grew to $12,282.50. 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 $7,500 in a savings account, and after 8 years, the balance grew to $12,282.50. 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

Given Values: We have: A = $12,282.50, P = $7,500, t = 8 years, n = 1 (compounded annually). Formula: A = P(1 + r/n)^(nt)Substitute into Formula: Substitute the values into the formula: 12,282.50 = 7,500(1 + r/1)^(1*8)Simplify Equation: Simplify the equation: 12,282.50 = 7,500(1 + r)^8Divide by 7,500: Divide both sides by 7,500: (12,282.50 / 7,500) = (1 + r)^8 1.6376667 = (1 + r)^8Take 8th Root: Take the 8th root of both sides to solve for (1 + r): (1.6376667)^(1/8) = 1 + r 1.063 = 1 + rSolve for (1 + r): Subtract 1 from both sides to solve for r: 1.063 - 1 = r r = 0.063Convert to Percentage: Convert r to a percentage: r = 0.063 * 100 r = 6.3%

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