After the last financial crisis, a company is obligated to make additional quarterly payments to an unfunded pension fund during the next $3$ years. The future value of those payments is to be $$899,000.$ Actuarial estimations project the fund to earn interest at the rate of $8$ percent per year. Payments are made at the end of each quarter. $($Use factor table in Appendix B for calculation$)$

Required $1$: What is the present value of the additional payments to be made to the pension fund? $

Required $2$: What is the amount of interest earned in the fourth period? $

Required $3$: What is the total amount of contributed towards the pension fund at the beginning of period $8?$ $

Required $4$: What is the total amount contributed towards the pension fund at the end of period $8$ inmediately after the $8$th payment was made? $

Required $5$: Assume the company had a very profitable year and at the moment of making the $10$th payment they decided to advance the remaining funds to achieve the total future value required by actuarial estimations. How much it must pay in dollars at the end of period $10$ and make no payments at the end of periods $11$ and $12?$ $