How much money must you invest now at $4.2 \%$ interest compounded continuously in order to have $\$ 10,000$ at the end of 4 years?

Step 1 ：We are given that the final amount (A) is $10,000, the annual interest rate (r) is 4.2% or 0.042 in decimal form, and the time (t) is 4 years. We need to find the principal amount (P) that needs to be invested now.

Step 2 ：We can use the formula for continuous compounding, which is \(A = P * e^{rt}\).

Step 3 ：We rearrange the formula to solve for P, which gives us \(P = \frac{A}{e^{rt}}\).

Step 4 ：Substituting the given values into the formula, we get \(P = \frac{10000}{e^{0.042*4}}\).

Step 5 ：Calculating the above expression, we find that \(P \approx 8453.54\).

Step 6 ：Final Answer: You must invest approximately \(\boxed{8453.54}\) now at 4.2% interest compounded continuously in order to have $10,000 at the end of 4 years.