Evelyn Aldana deposits a monthly income due for 5 years at a rate of 12% annual compounded monthly and you will not withdraw the money until 2 years later of the last income. If you can withdraw Q 90,000, how much do you deposit monthly?

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Answer to a math question Evelyn Aldana deposits a monthly income due for 5 years at a rate of 12% annual compounded monthly and you will not withdraw the money until 2 years later of the last income. If you can withdraw Q 90,000, how much do you deposit monthly?

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Ali

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$90000=\frac{ x \times \left( {\left( 1+0.01 \right)}^{2 \times 12}-1 \right) }{ \frac{ 0.12 }{ 12 } }$

$90000=\frac{ x \times \left( {\left( 1+0.01 \right)}^{24}-1 \right) }{ \frac{ 0.12 }{ 12 } }$

$90000=\frac{ x \times \left( {\left( 1+0.01 \right)}^{24}-1 \right) }{ 0.01 }$

$90000=\frac{ x \times \left( {1.01}^{24}-1 \right) }{ 0.01 }$

$90000=\frac{ x \times \left( {1.01}^{24}-1 \right) }{ \frac{ 1 }{ 100 } }$

$90000=\frac{ x \times \left( {\left( \frac{ 101 }{ 100 } \right)}^{24}-1 \right) }{ \frac{ 1 }{ 100 } }$

$90000=\frac{ x \times \left( \frac{ {101}^{24} }{ {100}^{24} }-1 \right) }{ \frac{ 1 }{ 100 } }$

$90000=\frac{ \frac{ {101}^{24}x }{ {100}^{24} }-x }{ \frac{ 1 }{ 100 } }$

$90000=\frac{ \frac{ {101}^{24}x-{100}^{24}x }{ {100}^{24} } }{ \frac{ 1 }{ 100 } }$

$90000=\frac{ {101}^{24}x-{100}^{24}x }{ {100}^{23} }$

$90000 \times {100}^{23}={101}^{24}x-{100}^{24}x$

${101}^{24}x-{100}^{24}x=90000 \times {100}^{23}$

$\left( {101}^{24}-{100}^{24} \right)x=90000 \times {100}^{23}$

$\begin{align*} & x=\frac{ 90000 \times{100}^{23} }{ {101}^{24}-{100}^{24} } \\ & x\approx3336.61\end{align*}$

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