The Jenkins family wants to save money to travel the world. They plan to Invest in an ordinary annuity that earns \( 4,8 \% \) interest, compounded annually, Payments will be made at the end of each year. How much money do they need to pay into the annulty each year for the annuity to have a total value of \( \$ 13,000 \) after 13 years? Do not round intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the list of financial formulas.

To find out how much money the Jenkins family needs to pay into the annuity each year for it to have a total value of $13,000 after 13 years, we can use the formula for the future value of an ordinary annuity: \[ FV = PMT \times \frac{(1 + r)^n - 1}{r} \] Where: - \( FV \) is the future value of the annuity - \( PMT \) is the annual payment - \( r \) is the annual interest rate - \( n \) is the number of years Given: - \( FV = \$13,000 \) - \( r = 4.8\% = 0.048 \) - \( n = 13 \) years We need to solve for \( PMT \) using the formula above. Solve the equation by following steps: - step0: Solve for \(PMT\): \(13000=\frac{PMT \left(\left(1+0.048\right)^{13}-1\right)}{0.048}\) - step1: Simplify: \(13000=\frac{\left(131^{13}-125^{13}\right)PMT }{6\times 125^{12}}\) - step2: Swap the sides: \(\frac{\left(131^{13}-125^{13}\right)PMT }{6\times 125^{12}}=13000\) - step3: Cross multiply: \(\left(131^{13}-125^{13}\right)PMT =6\times 125^{12}\times 13000\) - step4: Simplify the equation: \(\left(131^{13}-125^{13}\right)PMT =78000\times 125^{12}\) - step5: Divide both sides: \(\frac{\left(131^{13}-125^{13}\right)PMT }{131^{13}-125^{13}}=\frac{78000\times 125^{12}}{131^{13}-125^{13}}\) - step6: Divide the numbers: \(PMT =\frac{78000\times 125^{12}}{131^{13}-125^{13}}\) The Jenkins family needs to pay approximately $743.31 into the annuity each year for it to have a total value of $13,000 after 13 years.