Chris Silvers is 39 years old and has accumulated $128,000 in his self-directed defined contribution pension plan. Each year he contributes $2,500 to the plan, and his employer contributes an equal amount. Chris thinks he will retire at age 62 and figures he will live to age 86. 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 11% and has a standard deviation of 37%. Chris now has 25% of his money in the risk-free investment and 75% 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 can Chris expect to have in his risky account at retirement?

A) $1,400,326
B) $1,309,529
C) $1,543,781
D) $1,224,651
E) $1,345,886

Question

Kimani Black · Accepted Answer

Final Answer : A, Explanation :  The correct answer is A. $1,400,326.The expected return of the risky investment is 11%, and the standard deviation is 37%. Chris has 75% of his money in the risky investment, so the expected return of his portfolio is 0.75 * 11% + 0.25 * 4% = 9.25%. The standard deviation of his portfolio is 0.75 * 37% = 27.75%.Chris is 39 years old and plans to retire at age 62, so he has 23 years until retirement. He contributes $2,500 to the plan each year, and his employer contributes an equal amount, so he contributes a total of $5,000 to the plan each year.The future value of his risky investment at retirement can be calculated using the following formula:FV = PV * (1 + r)^nwhere:* FV is the future value* PV is the present value* r is the annual rate of return* n is the number of yearsIn this case, the present value is $128,000, the annual rate of return is 9.25%, and the number of years is 23. Plugging these values into the formula, we get:FV = $128,000 * (1 + 0.0925)^23FV = $1,400,326Therefore, Chris can expect to have $1,400,326 in his risky account at retirement.

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