Bill, age $45,$ wants to retire at age

$60.$ He currently earns $$60,000$ per

year. His goal is to replace $80\%$ of his

preretirement income. He wants the

retirement income to be adjusted for

inflation. Bill has an investment

portfolio valued at $$150,000,$ which is

currently earning $10\%$ average annual

returns. Bill expects inflation to

average $3\%$ and, based on his family

health, predicts he will live to age $90.$

Bill is currently saving $7\%$ of his gross

income at each year$-$end and expects

to continue this level of savings. Bill

wants to ignore any Social Security

benefits for purposes of retirement

planning.

How much total capital will Bill

need at age $60?$

A$.$ $$1,234,523\mathrm{.}37$

B$.$ $$1,034,278\mathrm{.}12$

C$.$ $$1,011,685\mathrm{.}49$

D$.$ $$1,016,984\mathrm{.}35$