Question

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.

Answer 1

Step 1

State the formula for annuities

`P_o=(d(1-(1+(r)/(k))^(-kn)))/((r)/(k))`

Where;

`\begin{gathered} P_o=amount\text{ at start} \\ d=Regular\text{ withdrawal=45000} \\ r=(10)/(100)=0.1 \\ n=25 \\ k=1 \end{gathered}`

Step 2

Find the amount that will be there at the beginning

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

Answer;

`P_o=\text{ \$408466.80}`