Moses' goal, when he retires from work in seven years, is to have $400,000 in his Retirement Fund. Assuming he achieves his goal and the fund earns 7% compounded semi-annually after he retires, Moses will, at the end of every six months, take $20,000 out of his Retirement Fund. For how long will he be able to do that before the money runs out?

A) 15.4 years
B) 35.0 years
C) 20.0 years
D) 12.9 years
E) 17.5 years

To solve this, we use the formula for the present value of an annuity because Moses is withdrawing a fixed amount periodically, and the fund earns a fixed interest rate. The formula is: $$PV=P\times \left[\frac{1-(1+r{)}^{-n}}{r}\right]$$ Where:- $PV$ is the present value or the initial amount in the retirement fund ($400,000),- $P$ is the payment amount per period ($20,000),- $r$ is the interest rate per period (7% per year compounded semi-annually gives 3.5% per period, or 0.035),- $n$ is the total number of payments.Rearranging the formula to solve for $n$ : $$n=\frac{\log (1-\frac{PV\times r}{P})}{\log (1+r)}$$ Plugging in the values: $$n=\frac{\log (1-\frac{400,000\times 0.035}{20,000})}{\log (1+0.035)}$$$$n=\frac{\log (1-0.7)}{\log (1.035)}$$$$n=\frac{\log (0.3)}{\log (1.035)}$$$$n\approx 35$$ Since $n$ represents the total number of semi-annual payments, to find the number of years, we divide by 2: $$\text{Years}=\frac{35}{2}=17.5$$ Therefore, Moses will be able to withdraw $20,000 every six months for approximately 17.5 years before the money runs out.