Two partners agree to invest equal amounts in their business. One will contribute $\$ 10,000$ immediately. The other plans to contribute an equivalent amount in 7 years. How much should she contribute at that time to match her partner's investment now, assuming an interest rate of $3 \%$ compounded quarterly?
(Type an integer or decimal rounded to two decimal places as needed.)

Step 1 ：The problem is asking for the future value of the initial investment after 7 years, given a quarterly compounded interest rate of 3%. The formula for future value (FV) is: \(FV = PV * (1 + r/n)^{nt}\) where: PV is the present value (the initial investment), r is the annual interest rate (in decimal form), 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 2 ：In this case, PV = $10,000, r = 3% = 0.03, n = 4 (quarterly compounding), and t = 7 years. We can plug these values into the formula to find the future value.

Step 3 ：Substituting the given values into the formula, we get: \(FV = 10000 * (1 + 0.03/4)^{4*7}\)

Step 4 ：Solving the above expression, we find that the future value of the initial investment after 7 years, given a quarterly compounded interest rate of 3%, is approximately $12,327.12. This is the amount the second partner should contribute in 7 years to match the first partner's initial investment.

Step 5 ：Final Answer: The second partner should contribute approximately \(\boxed{12327.12}\) in 7 years to match the first partner's initial investment.