Question
Find \( A \) in the equation below \[ A=500\left(1+\frac{0.21}{12}\right)^{12} \]
Ask by Page Lawson. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( A \) is approximately 615.72.
Solution
Calculate or simplify the expression \( 500*(1+0.21/12)^{12} \).
Calculate the value by following steps:
- step0: Calculate:
\(500\left(1+\frac{0.21}{12}\right)^{12}\)
- step1: Divide the terms:
\(500\left(1+\frac{7}{400}\right)^{12}\)
- step2: Add the numbers:
\(500\left(\frac{407}{400}\right)^{12}\)
- step3: Simplify:
\(500\times \frac{407^{12}}{400^{12}}\)
- step4: Rewrite the expression:
\(100\times 5\times \frac{407^{12}}{400^{12}}\)
- step5: Rewrite the expression:
\(100\times 5\times \frac{407^{12}}{100^{12}\times 4^{12}}\)
- step6: Reduce the numbers:
\(5\times \frac{407^{12}}{100^{11}\times 4^{12}}\)
- step7: Rewrite the expression:
\(5\times \frac{407^{12}}{25^{11}\times 4^{11}\times 4^{12}}\)
- step8: Rewrite the expression:
\(5\times \frac{407^{12}}{5^{22}\times 4^{11}\times 4^{12}}\)
- step9: Reduce the numbers:
\(1\times \frac{407^{12}}{5^{21}\times 4^{11}\times 4^{12}}\)
- step10: Multiply the fractions:
\(\frac{407^{12}}{5^{21}\times 4^{23}}\)
The value of \( A \) in the equation \( A=500\left(1+\frac{0.21}{12}\right)^{12} \) is approximately 615.719657.
Reviewed and approved by the UpStudy tutoring team
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Bonus Knowledge
To find \( A \), we can start by simplifying the expression. First, we calculate \( \frac{0.21}{12} \): \[ \frac{0.21}{12} = 0.0175 \] Now, we add 1 to this value: \[ 1 + 0.0175 = 1.0175 \] Next, raise \( 1.0175 \) to the 12th power: \[ (1.0175)^{12} \approx 1.2314 \] Now, we multiply this result by 500: \[ A \approx 500 \times 1.2314 \approx 615.70 \] Therefore, the value of \( A \) is approximately \( 615.70 \).