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.
-How much does Alan currently have in the safe account; how much in the risky account?
A)$31,200, $46,800
B)$39,000, $39,000
C)$15,900, $62,100
D)$45,300, $32,700
E)$64,000,$14,000

Question

Quizplus · Accepted Answer

Let X be the amount invested in the risk-free account, and Y be the amount invested in the risky account. We know that:

X + Y = $78,000 (total amount accumulated)
Y/X = 60/40 = 3/2 (proportion invested in risky account is 1.5 times that in the safe account)

Solving these two equations simultaneously, we get:

X = $31,200
Y = $46,800

Therefore, Alan currently has $31,200 in the safe account and $46,800 in the risky account.

As for the best choice(s), it depends on Alan's risk tolerance and investment objectives. The risky investment offers a higher expected return but also has more risk (as indicated by its standard deviation). If Alan is willing to take on more risk for potentially higher returns, then the 60/40 allocation in favor of the risky investment may be appropriate. However, if he is more risk-averse, then he may want to consider shifting more of his assets into the safe investment, even though it offers a lower expected return. Ultimately, the best choice depends on Alan's personal circumstances and preferences.

Alan Barnett Is 43 Years Old and Has Accumulated $78,000