Rochelle deposits $\$ 4,000$ in an IRA. What will be the value (1n dollars) of her investment in 25 years if the investment is earning $6 \%$ per year and is compounded continuously? (Simplify your answer completely. Round your answer to the nearest cent.)

Step 1 ：Given that Rochelle deposits $4000 in an IRA, the annual interest rate is 6% or 0.06 in decimal, and the time of investment is 25 years.

Step 2 ：Using the formula for continuous compounding, which is \(A = P * e^{rt}\), where \(A\) is the amount of money accumulated after n years, including interest, \(P\) 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 ：Substitute the given values into the formula: \(A = 4000 * e^{0.06 * 25}\)

Step 4 ：Calculate the value of \(A\) to find the value of the investment after 25 years.

Step 5 ：\(A = 17926.756281352256\)

Step 6 ：Round the final answer to the nearest cent.

Step 7 ：Final Answer: The value of Rochelle's investment in 25 years will be approximately \(\boxed{17926.76}\).