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 the Jenkins family needs to invest annually in their ordinary annuity to reach a total of $13,000 after 13 years at an interest rate of 4.8%, we can use the future value of an ordinary annuity formula: \[ FV = P \times \frac{(1 + r)^n - 1}{r} \] where: - \( FV \) is the future value of the annuity, which is $13,000 - \( P \) is the annual payment (the amount we want to find) - \( r \) is the annual interest rate (4.8% or 0.048) - \( n \) is the number of years of payments (13) Now, plugging in the values we have: \[ 13000 = P \times \frac{(1 + 0.048)^{13} - 1}{0.048} \] Calculating the compound interest factor: \[ (1 + 0.048)^{13} = 1.706542 \] So, we have: \[ 13000 = P \times \frac{1.706542 - 1}{0.048} \] \[ 13000 = P \times \frac{0.706542}{0.048} \] \[ 13000 = P \times 14.72425833 \] Now, solving for \( P \): \[ P = \frac{13000}{14.72425833} \approx 882.91 \] The Jenkins family needs to invest approximately **$882.91** at the end of each year in the annuity to reach their goal of $13,000 in 13 years.