Dusty Jones is 23 years old and has accumulated $4,000 in her self-directed defined contribution pension plan. Each year she contributes $2,000 to the plan, and her employer contributes an equal amount. Dusty thinks she will retire at age 67 and figures she will live to age 81. The plan allows for two types of investments. One offers a 3.5% risk-free real rate of return. The other offers an expected return of 10% and has a standard deviation of 23%. Dusty now has 5% of her money in the risk-free investment and 95% in the risky investment. She plans to continue saving at the same rate and keep the same proportions invested in each of the investments. Her salary will grow at the same rate as inflation. How much can Dusty expect to have in her risky account at retirement?
A) $2,731,838
B) $2,915,415
C) $1,425,316
D) $224,651
E) $3,545,886

Question

Quizplus · Accepted Answer

The correct answer is A. $2,731,838.The expected return of the risky investment is 10%, and the standard deviation is 23%. Dusty has 95% of her money in the risky investment, so the expected return of her portfolio is 9.5%. The risk-free rate is 3.5%, so the expected excess return of her portfolio is 6%.Dusty is saving $4,000 per year, and her employer is contributing an equal amount. She plans to retire in 44 years (age 67 - age 23), and she figures she will live to age 81. So, she will have 14 years of retirement.The future value of her savings at retirement can be calculated using the following formula:FV = PV * (1 + r)^nwhere:FV is the future valuePV is the present valuer is the annual interest raten is the number of yearsThe present value of her savings is $4,000. The annual interest rate is 9.5%. The number of years is 44. So, the future value of her savings at retirement is:FV = $4,000 * (1 + 0.095)^44= $2,731,838Therefore, Dusty can expect to have $2,731,838 in her risky account at retirement.

Dusty Jones Is 23 Years Old and Has Accumulated $4,000