An amount of \( \$ 19,000 \) is borrowed for 9 years at \( 4.5 \% \) interest, compounded annually. Assuming that no payments are made, find the amount owed after 9 years. Use the calculator provided and round your answer to the nearest dollar.
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To calculate the future amount owed after 9 years with \( \$19,000 \) borrowed at \( 4.5\% \) annual interest compounded annually, you can use the formula for compound interest: \[ A = P(1 + r)^n \] Where: - \( A \) is the amount owed after \( n \) years, - \( P = 19000 \) (the principal), - \( r = 0.045 \) (the annual interest rate), - \( n = 9 \) (the number of years). Plugging in the values, we get: \[ A = 19000(1 + 0.045)^9 \] Calculating it step by step: 1. Calculate \(1 + 0.045 = 1.045\). 2. Raise \(1.045\) to the power of \(9\): \(1.045^9 ≈ 1.432364654\). 3. Multiply \(19,000\) by \(1.432364654\): \[ A = 19000 \times 1.432364654 ≈ 27214.91. \] Rounding to the nearest dollar, the amount owed after 9 years is approximately \( \$27,215 \).
