A $52-$year$-$old client asks an accountant how to plan for his future retirement at age

$62.$ He expects income from Social Security in the amount of $$21,600$ per year and a retirement

pension of $$40,500$ per year from his employer. He wants to make monthly contributions to an

investment plan that pays $8\%$ compounded monthly for $10$ years $($that is$,$ the annual rate is $8\%,$

hence the monthly compounded rate is $8\%/12=0\mathrm{.}67\%$ so that he will have a total income of

$$83,700$ per year for $30$ years. What must the size of the monthly contributions be to accomplish

this goal, if it is assumed that money will be worth $8\%$ compounded continuously throughout the

period after he is $62?$

To help you answer this question, complete the following.

$1.$ How much money must the client withdraw annually from his investment plan during his

retirement so that his total income goal is met?How much money S must the client's account contain when he is $62$ so that it will generate this

annual amount for $30$ years? $($Hint: S can be considered the present value over $30$ years of a

continuous income stream with the amount you found in Question $1$ as its annual rate of flow.$)$