1) Ms. Warden needs $\$ 20000$ to go on her dream vacation in four years. How much does she need to invest now in an account earning $8.5 \%$ annual interest compounded semi-annually? [3]

Step 1 ：Translate the problem into the formula for the present value of an investment: \(PV = \frac{FV}{(1 + \frac{r}{n})^{nt}}\), where PV is the present value, FV is the future value, r is the annual interest rate (in decimal form), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.

Step 2 ：Substitute the given values into the formula: FV = $20000, r = 8.5% = 0.085, n = 2 (since interest is compounded semi-annually), and t = 4 years.

Step 3 ：Calculate the present value: \(PV = \frac{20000}{(1 + \frac{0.085}{2})^{2*4}}\)

Step 4 ：Simplify the expression to get the final answer: Ms. Warden needs to invest approximately $14335.79 now to have $20000 in four years in an account earning 8.5% annual interest compounded semi-annually.

Step 5 ：Final Answer: \(\boxed{14335.79}\)