Saving for retirement.

Suppose you have decided to set up a personal pension fund for your retirement. You have just turned 25. You expect to retire at age 65 and believe it is reasonable to count on living at least 20 years after retirement. Furthermore, you wish to have an annual income of $100,000 during your retirement starting when you turn 65 and that upon receipt of the 20th 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 promises to yield on average a 12 percent rate and (2) a conservative portfolio of government bonds that promises 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?