Tyra invests $\$ 5100$ in a new savings account which earns $4.8 \%$ annual interest, compounded quarterly. What will be the value of her investment after 2 years? Round to the nearest cent. Interest formulas

Step 1 ：Given that Tyra invests $5100 in a new savings account which earns 4.8% annual interest, compounded quarterly. We are asked to find the value of her investment after 2 years.

Step 2 ：We can use the formula for compound interest to solve this problem. The formula is: \(A = P (1 + \frac{r}{n})^{nt}\)

Step 3 ：In this formula: \(A\) 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. \(t\) is the time the money is invested for in years.

Step 4 ：Substitute the given values into the formula: \(P = 5100\), \(r = 0.048\), \(n = 4\), and \(t = 2\) years.

Step 5 ：Calculate the future value of the investment: \(A = 5100 (1 + \frac{0.048}{4})^{4*2}\)

Step 6 ：Solving the above expression gives \(A = 5610.664191046283\)

Step 7 ：Rounding to the nearest cent, the value of her investment after 2 years will be approximately \(\boxed{5610.66}\)