Sam is currently $30$ years of age. He owns his own business and wants to retire at the age of $65.$ He has little confidence in the current Social Security system. He opens a Roth IRA and invests in a small$-$cap stock mutual fund his retirement. The stock mutual fund earns $13\%$ on average. He wants to retire with an annual income of $$90,000$ a year. At retirement, the fund will be shifted to a large$-$cap stock mutual fund earning $9\%$ on average. He believes he will live to age $90.$

How much does he have to accumulate by the time he reaches age $65$ to receive $$90,000$ at the beginning of each year for the rest of his life?

a$.$

$$963,595\mathrm{.}06$

b$.$

$$875,405\mathrm{.}23$

c$.$

$$884,032\mathrm{.}16$

d$.$

$$810,560\mathrm{.}40$