Following the birth of a child, a parent wants to make an initial investment $P_0$ that will grow to $\mathrm{\$}50,000$ for the child's education at age 18. Interest is compounded continuously at $5\mathrm{\%}$. What should the initial investment be? Such an amount is called the present value of $\mathrm{\$}50,000$ due 18 years from now.

Step 1 ：A parent wants to make an initial investment $P_0$ that will grow to $50,000 for their child's education at age 18. The interest is compounded continuously at a rate of 5%.

Step 2 ：The formula for continuous compounding is given by: $$A=P_0{e}^{rt}$$ where: $A$ is the amount of money accumulated after n years, including interest, $P_0$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (in decimal), and $t$ is the time the money is invested for, in years.

Step 3 ：In this case, we know that $A=\mathrm{\$}50,000$, $r=5\mathrm{\%}=0.05$, and $t=18$ years. We need to find $P_0$.

Step 4 ：We can rearrange the formula to solve for $P_0$: $$P_0=\frac{A}{e^{rt}}$$

Step 5 ：Substituting the given values into the formula, we get: $$P_0=\frac{50000}{e^{0.05\ast 18}}$$

Step 6 ：Solving the above expression, we find that the initial investment should be approximately $\boxed{{\displaystyle 20328.48}}$.