9.5. A self-employed investor who has just turned 35 wants to save for his retirement with a Keogh account. He plans to retire on his 65th birthday and wants a monthly income, beginning the month after his 65th birthday, of $2,000 (after taxes) until he dies.

• He has budgeted conservatively, assuming that he will die at age 95.

• Assume that until he reaches age 65, the Keogh account earns 8 percent interest, compounded annually, which accumulates tax free.

• At age 65, assume that the interest accumulated in the Keogh account pays a lump-sum tax at a rate of 30 percent.

• Thereafter, assume that the investor is in a 0 percent tax bracket and that the interest on his account earns 7 percent interest, compounded monthly.

How much should the investor deposit annually in his Keogh account beginning on his 35th birthday and ending on his 64th birthday to finance his retirement?