Suppose that you have a brother who is $36$ today and that his salary for the year ending today is

$$135,000.$ Suppose that he is paid on an annual basis at the end of each year and that he will

receive $$135,000$ today $($reflecting his salary for the past year$$s work$),$ out of which he will make

a deposit to his account. He plans to retire at age $70($when he will earn his last salary and make

his last deposit into his retirement account$)$ and will make annual withdrawals from his account

beginning at age $71$ with an additional withdrawal each subseqent year. He expects the first

withdrawal at $71$ to be $85\%$ of his salary from the last year that he works $($or $70).$ All living

expenses between now and retirement will be covered by his annual salary. All living expenses

after retirement will be covered by his withdrawals from his retirement account each year, except

for the medical expenses described below. He has saved $$400,000$ to date. Assume that he will

save $16\%$ of his annual income while he works, and that he will not save any additional amount

after he retires $($although he will continue to earn a return on his investments$).$

Assume that, given the state of health care costs and a family history of healthcare issues, he will

need to have an amount of $$500,000$ available by age $66$ to cover healthcare costs above and

beyond what his health insurance plan is likely to cover. Treat this figure as an expected one$-$

time outflow at this point. Of course, actual future health care costs are unlikely to be a one$-$time

event and to differ from this amount. What we are doing is treating the $$500,000$ as the present

$($or future$)$ value at age $66$ of all possible additional costs over time. Save based on the prediction

that the one$-$time expense will occur at that time. Assume that these health care costs will be paid

out of his retirement account.

You project that his salary will grow at a rate of $5\%$ and that his retirement living expenses will

grow at $2\mathrm{.}5\%$ to reflect long$-$term inflation forecasts. The higher growth rate in his salary reflects

your expectation that he will receive promotions and performance raises and that absent

promotions and performance pay his salary will keep pace with inflation. The appropriate

interest rate for his working life is $8\%$ and declines to $5\mathrm{.}75\%$ after he retires. Both rates of return

are nominal $($i$.$e$.,$ include compensation for expected inflation$).$ Thus you will not need to adjust

the rates of return for expected inflation.

Assume that he will live until age $88$ and that he wishes to have a balance of $$2$ million

remaining at $88.$ This balance is available as a safety net if he lives longer than expected and as a

bequest to his children if he doesn$$t live past $88.$

He would like to build a retirement home at age $60$ in coastal North Carolina using funds from

his retirement account. Based on his saving behavior and expected needs, how much could he

afford to spend on the home at that time? Assume that other housing needs will be covered by his

salary while he works. Ignore the residual value of the house at $88.$ We will assume that he could

sell the house for funds if he lives longer than expected or leave it to his children $($in addition to

the $$2$ million mentioned above$)$ if he doesn$$t live past $88.$