provide answers for all parts please

Problem #4 You must provide the appropriate formulas discussed in class along with the necessary computations in order to receive credit. Simply providing an answer will result in zero credit. a. Mary wants to have a retirement fund of $500,000. She plans on retiring at age 65. Mary will invest an annuity amount on her birthday from age 55 through age 64. The fund will earn interest at a rate of 6%. Calculate the annuity amount to be invested in order for Mary to achieve her goal. b. Henry purchases equipment on January 1, 2021. According to the contract, Henry must make annuity payments of $5,000 starting on January 1, 2022 through January 1, 2028. Assume an interest rate of 4%. Calculate the cost of the equipment. c. Amy has $1 million in her investment fund. The fund earns interest at 5%. Amy will exhaust the fund by withdrawing equal annual amounts over the next fifteen years. What amount will Amy withdraw each year? d. John wants to withdraw $8,000 each year from July 1, 2025 through July 1, 2029. The investment fund earns interest at a rate of 2%. In order to make these withdrawals, John will invest an annuity on July 1, 2021 through July 1, 2024. Calculate the annuity John needs to invest each year