2 years ago, Rick invested $\$ 7,500.00$ in an account earning $5 \%$ compounded yearly. Now, he has found another account that will pay $7.25 \%$ compounding quarterly for a minimum commitment of 5 years. How much will Rick have if he invests all his money in the new account for the next 5 years? Assume the interest rates do not change while the respective accounts are open. Round to the nearest cent. Final Value CHECK ANSWER

Step 1 ：Given that Rick invested $7500 in an account with an annual interest rate of 7.25% compounded quarterly for 5 years, we are to find the future value of his investment.

Step 2 ：The formula for future value with compound interest is given by \(FV = P * (1 + r/n)^{nt}\), where \(FV\) is the future value of the investment, \(P\) is the principal amount, \(r\) 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 3 ：Substituting the given values into the formula, we have \(P = 7500\), \(r = 7.25\% = 0.0725\), \(n = 4\) (since interest is compounded quarterly), and \(t = 5\) years.

Step 4 ：Calculating the future value, we get \(FV = 7500 * (1 + 0.0725/4)^{4*5}\)

Step 5 ：Computing the above expression, we find that the future value of Rick's investment after 5 years in the new account, rounded to the nearest cent, is \(\boxed{\$10,741.95}\)