Step 1 :We are given a future value of the annuity as $49,000, an annual interest rate of 8% or 0.08, the interest is compounded 12 times a year, and the time period is 5 years. We are asked to find the payment made each period.
Step 2 :We use the formula for the future value of an ordinary annuity: \(FV = P \times \frac{(1 + \frac{r}{n})^{nt} - 1}{\frac{r}{n}}\)
Step 3 :We rearrange this formula to solve for P: \(P = FV \times \frac{\frac{r}{n}}{(1 + \frac{r}{n})^{nt} - 1}\)
Step 4 :Substitute the given values into the formula: \(P = 49000 \times \frac{\frac{0.08}{12}}{(1 + \frac{0.08}{12})^{12 \times 5} - 1}\)
Step 5 :Solving the above expression, we get \(P = 666.876653465612\)
Step 6 :Rounding to the nearest cent, we get the final answer: \(\boxed{\$666.88}\)