Find $$ A $$ in the equation below $$ A=5000\left(1+\frac{0.123}{2}\right)^{6} $$

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UpStudy AI · Accepted Answer

Calculate or simplify the expression $$ 5000*(1+0.123/2)^6 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$5000\left(1+\frac{0.123}{2}ight)^{6}$$
- step1: Divide the terms:
  $$5000\left(1+\frac{123}{2000}ight)^{6}$$
- step2: Add the numbers:
  $$5000\left(\frac{2123}{2000}ight)^{6}$$
- step3: Simplify:
  $$5000	imes \frac{2123^{6}}{2000^{6}}$$
- step4: Rewrite the expression:
  $$1000	imes 5	imes \frac{2123^{6}}{2000^{6}}$$
- step5: Rewrite the expression:
  $$1000	imes 5	imes \frac{2123^{6}}{1000^{6}	imes 2^{6}}$$
- step6: Reduce the numbers:
  $$5	imes \frac{2123^{6}}{1000^{5}	imes 2^{6}}$$
- step7: Rewrite the expression:
  $$5	imes \frac{2123^{6}}{125^{5}	imes 8^{5}	imes 2^{6}}$$
- step8: Rewrite the expression:
  $$5	imes \frac{2123^{6}}{5^{15}	imes 8^{5}	imes 2^{6}}$$
- step9: Reduce the numbers:
  $$1	imes \frac{2123^{6}}{5^{14}	imes 8^{5}	imes 2^{6}}$$
- step10: Multiply the fractions:
  $$\frac{2123^{6}}{2^{21}	imes 5^{14}}$$
The value of $$ A $$ in the equation $$ A=5000\left(1+\frac{0.123}{2}ight)^{6} $$ is approximately 7153.029158.
$$ A $$ is approximately 7153.03.

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