A $\$ 5222.39$ investment matures in 5 years, 10 months. Find the maturity value if interest is 2.8 \%$ per annum compounded quarterly.
The maturity value is $\$$
(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Step 1 ：Given that the principal amount (P) is $5222.39, the annual interest rate (r) is 2.8\%, the number of times that interest is compounded per year (n) is 4 (quarterly), and the time the money is invested for (t) is 5 years and 10 months (or 5.8333 years).

Step 2 ：We can calculate the maturity value (A) using the formula for compound interest: \(A = P (1 + \frac{r}{n})^{nt}\)

Step 3 ：Substitute the given values into the formula: \(A = 5222.39 (1 + \frac{0.028}{4})^{4*5.8333}\)

Step 4 ：Calculate the value inside the parentheses: \(1 + \frac{0.028}{4} = 1.007\)

Step 5 ：Substitute this value back into the formula: \(A = 5222.39 * (1.007)^{4*5.8333}\)

Step 6 ：Calculate the exponent: \(4*5.8333 = 23.3332\)

Step 7 ：Substitute this value back into the formula: \(A = 5222.39 * (1.007)^{23.3332}\)

Step 8 ：Calculate the final value: \(A = 6145.496099827384\)

Step 9 ：Round the final answer to the nearest cent: \(A = 6145.50\)

Step 10 ：Final Answer: The maturity value is \(\boxed{6145.50}\)