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You want to be able to withdraw $45,000 each year for 25 years. Your account earns 10% interest. How much do you need in your account at the beginning?The answer is given as: 408466.80I just need the breakdown on how to get this answer.

You want to be able to withdraw 45000 each year for 25 years Your account earns 10 interest How much do you need in your account at the beginningThe answer is g class=

Respuesta :

Step 1

State the formula for annuities

[tex]P_o=\frac{d(1-(1+\frac{r}{k})^{-kn})}{\frac{r}{k}}[/tex]

Where;

[tex]\begin{gathered} P_o=amount\text{ at start} \\ d=Regular\text{ withdrawal=45000} \\ r=\frac{10}{100}=0.1 \\ n=25 \\ k=1 \end{gathered}[/tex]

Step 2

Find the amount that will be there at the beginning

[tex]P_o=\frac{45000(1-(1+\frac{0.1}{1})^{-1(25)})}{\frac{0.1}{1}}[/tex][tex]\begin{gathered} P_o=\frac{45000(1-(1.1)^{-25})}{0.1} \\ P_o=\frac{40846.68008}{0.1} \\ P_o=\text{\$408466.8008} \\ P_o\approx\text{\$408466.80} \end{gathered}[/tex]

Answer;

[tex]P_o=\text{ \$408466.80}[/tex]

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