Step 1 :Translate the given problem into the formula for the present value of an investment: PV = FV / (1 + r/n)^(nt).
Step 2 :Identify the given values: Future Value (FV) is \$20,500, the annual interest rate (r) is 3.5% or 0.035 in decimal form, the number of times interest is compounded per year (n) is 52 (since it's compounded weekly), and the time the money is invested for (t) is 6 years.
Step 3 :Substitute the given values into the formula: PV = 20500 / (1 + 0.035/52)^(52*6).
Step 4 :Solve the equation to find the present value (PV).
Step 5 :Round the answer to the nearest penny to find that Elizabeth needs to deposit \$16,618.16 today in order to have \$20,500 in 6 years.
Step 6 :\(\boxed{\$16,618.16}\) is the final answer.