Wendy has set up an ordinary annuity to save for a retirement home in 15 years. If her monthly payments are $\mathrm{\$}600$ and the annuity has an annual interest rate of $6.6\mathrm{\%}$, what will be the value of the annuity when she retires?

The value of Wendy's annuity when she retires will be $\mathrm{\$}◻$.
(Round to the nearest cent as needed.)
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Step 1 ：Define the variables where P is the annual payment, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years. In this case, P equals to $600times12whichis$7200, r equals to 6.6% or 0.066, n equals to 1, and t equals to 15 years.

Step 2 ：Calculate the value of the annuity using the formula $A=P\times \left(\frac{(1+r/n{)}^{n\times t}-1}{r/n}\right)$.

Step 3 ：Substitute the values into the formula to get $A=7200\times \left(\frac{(1+0.066/1{)}^{1\times 15}-1}{0.066/1}\right)$.

Step 4 ：Solve the equation to find the value of A, which is approximately $175451.26.

Step 5 ：Final Answer: The value of Wendy's annuity when she retires will be $\boxed{{\displaystyle \mathrm{\$}175,451.26}}$.