Suppose you are $35$ years old, and plan to retire in $30$ years. You want to receive $$6,500$ per month in retirement and the first withdraw will be made when you turn $65.$ If you can earn $8\%$ APR and you expect to need the income for $20$ years. To accumulate the retirement money you need when you turn $65,$ you plan to make the same deposit every month starting today $(t=0)$ and the last monthly deposit will be made just one month before you turn $65.$ What should your monthly deposit be to accumulate the needed money for your retirement?

$$367\mathrm{.}14$

$$521\mathrm{.}42$

$$565\mathrm{.}08$

Answer can not be found.

$$524\mathrm{.}90$