Alex Moore 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. Alex 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 $34\%.$ Alex 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 can Alex be sure of having in the safe account at retirement?