Wendy has set up an ordinary annuity to save for a retirement home in 15 years. If her monthly payments are $\$ 600$ and the annuity has an annual interest rate of $6.6 \%$, what will be the value of the annuity when she retires? The value of Wendy's annuity when she retires will be $\$ \square$. (Round to the nearest cent as needed.) Get more help - Clear all Check answer

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 $600 times 12 which is $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 \(\boxed{\$175,451.26}\).