Alan Barnett is 43 years old and has accumulated $78,000 in his self-directed defined
contribution pension plan. Each year he contributes $1,500 to the plan and his employer
contributes an equal amount. Alan thinks he will retire at age 60 and figures he will live to
age 83. The plan allows for two types of investments. One offers a 4% risk-free real rate of
return. The other offers an expected return of 10% and has a standard deviation of 34%.
Alan now has 40% of his money in the risk-free investment and 60% in the risky
investment. He plans to continue saving at the same rate and keep the same proportions
invested in each of the investments. His salary will grow at the same rate as inflation.
Of the total amount of new funds that will be invested by Alan and by his employer on his
behalf, how much will he put into the safe account each year; how much into the risky
account?