A credit union client deposits $\mathrm{\$}2,100$ in an account earning $5\mathrm{\%}$ interest, compounded quarterly. What will the balance of the account be at the end of 29 years?
Enter the answer in dollars and cents, and round to the nearest cent, if needed.

Step 1 ：The problem is asking for the future value of an investment given an initial deposit, an interest rate, and a time period. The formula for future value (FV) in the case of quarterly compounding is: $FV=P\ast (1+r/n{)}^{nt}$ where: P = principal amount (the initial amount of money), r = annual interest rate (in decimal), n = number of times that interest is compounded per year, t = time the money is invested for in years.

Step 2 ：In this case, P = $2,100, r = 5% = 0.05, n = 4 (since interest is compounded quarterly), and t = 29 years.

Step 3 ：Substitute the given values into the formula: $FV=2100\ast (1+0.05/4{)}^{4\ast 29}$

Step 4 ：Solving the equation gives: $FV=8872.43841639962$

Step 5 ：Rounding to the nearest cent, the final answer is: $\boxed{{\displaystyle 8872.44}}$