Suppose you have decided to set up a personal pension fund for your retirement.
You just turned twenty-five. You expect to retire at age sixty-five and believe it is reasonable to count on living at least twenty years after retirement. Furthermore, you wish to have an annual income of $100,000 during your retirement starting when you turn sixty-five, and that upon receipt of the twentieth payment, the entire capital sum would have been distributed. You have been offered two investment plans by your financial adviser:
(1) An "aggressive" portfolio of well-diversified equities that promise to yield on average a 12 percent rate and
(2) A "conservative" portfolio of government bonds that promise to yield on average a 6 percent rate.
a. How much must you invest in each of the two savings schemes each year, starting now until you retire, to ensure that you receive the $100,000 per year retirement income?
b. What investment strategy would you recommend?