What sum of money will grow to $4788.78 in nine years at 7.1% compounded annually?
The sum of money is $
(Round to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Step 1 ：The problem is asking for the initial amount of money that will grow to $4788.78 after 9 years with an annual interest rate of 7.1% compounded annually. This is a compound interest problem.

Step 2 ：The formula for compound interest is: \(A = P(1 + \frac{r}{n})^{nt}\) 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), \(n\) is the number of times that interest is compounded per year, and \(t\) is the time the money is invested for in years.

Step 3 ：In this case, we know \(A = 4788.78\), \(r = 0.071\), \(n = 1\), and \(t = 9\). We need to solve for \(P\).

Step 4 ：We can rearrange the formula to solve for \(P\): \(P = \frac{A}{(1 + \frac{r}{n})^{nt}}\)

Step 5 ：Substituting the known values into the formula gives: \(P = \frac{4788.78}{(1 + \frac{0.071}{1})^{1*9}}\)

Step 6 ：Solving for \(P\) gives: \(P = 2582.971701818878\)

Step 7 ：Rounding to the nearest cent gives: \(P = 2582.97\)

Step 8 ：Final Answer: The sum of money that will grow to $4788.78 in nine years at 7.1% compounded annually is approximately \(\boxed{2582.97}\)