Find the present value of an annuity with payments of $600 at the end of every three months for 9 years. The interest rate is 10% compounded quarterly

The present value of the annuity is $ (Round the final answer to the nearest cent as neededRound all intermediate values to six decimal places as needed)

Step 1 ：Given an annuity with payments of $600 at the end of every three months for 9 years. The interest rate is 10% compounded quarterly.

Step 2 ：The present value of an annuity can be calculated using the formula: $PV=P\ast [(1-(1+r{)}^{-n})/r]$ where: $PV$ is the present value, $P$ is the payment per period, $r$ is the interest rate per period, and $n$ is the number of periods.

Step 3 ：In this case, the payment per period ($P$) is $600, the interest rate per period ($r$) is 10% per year compounded quarterly (so 10%/4 = 2.5% or 0.025 per quarter), and the number of periods ($n$) is 9 years * 4 quarters/year = 36 quarters.

Step 4 ：Substitute these values into the formula: $P=600$, $r=0.025$, $n=36$.

Step 5 ：Calculate the present value: $PV=600\ast [(1-(1+0.025{)}^{-36})/0.025]$

Step 6 ：$PV=14133.750640772469$

Step 7 ：Round the final answer to the nearest cent: $\boxed{{\displaystyle 14133.75}}$