You invested $6,000 in a savings account, and after 7 years, the balance grew to $9,123.45. The interest is compounded annually. What is the annual interest rate? Use the formula A=P(1+nr)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.
Q. You invested $6,000 in a savings account, and after 7 years, the balance grew to $9,123.45. The interest is compounded annually. What is the annual interest rate? Use the formula A=P(1+nr)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.
Given Values: We have: A = 9,123.45, P = 6,000, t = 7 years, n = 1 (compounded annually). Formula: A=P(1+nr)nt
Substitute into Formula: Substitute the values into the formula: 9,123.45=6,000(1+1r)1⋅7
Simplify Equation: Simplify the equation: 9,123.45=6,000(1+r)7
Divide by 6,000: Divide both sides by 6,000: (9,123.45/6,000)=(1+r)71.520575=(1+r)7
Take 7th Root: Take the 7th root of both sides to solve for (1+r): (1.520575)(1/7)=1+r1.060=1+r
Subtract 1 for r: Subtract 1 from both sides to solve for r: 1.060−1=rr=0.060
Convert to Percentage: Convert r to a percentage: r=0.060imes100r=6.0extextpercent
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