To calculate the amount in the account after 26 years with an initial principal (P) of $6,900, an annual interest rate (r) of 8.25%, and assuming the interest is compounded annually, we can use the formula for compound interest:
\[ A = P(1 + r)^t \]
where:
- \(A\) is the amount in the account after time \(t\),
- \(P\) is the principal amount (initial investment),
- \(r\) is the annual interest rate (as a decimal),
- \(t\) is the number of years the money is invested for.
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Convert the interest rate from a percentage to a decimal: \[ r = \frac{8.25}{100} = 0.0825 \]
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Plug the values into the formula: \[ A = 6900(1 + 0.0825)^{26} \] \[ A = 6900(1.0825)^{26} \]
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Calculate \( (1.0825)^{26} \): \[ (1.0825)^{26} \approx 6.778263 \]
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Now calculate \(A\): \[ A \approx 6900 \times 6.778263 \approx 46678.12 \]
The amount in the account after 26 years, rounded to the nearest cent, is approximately $46,678.12.
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