a) Mary Hartwell just started her retirement plan. She decided to make equal annual deposits for 30 years. She will then receive payments of $30,000.00 at the end of each of the following 20 years (the first payment will be at t=31). Mary and her insurance company agreed that her account would earn annual interest of 10% for the life of the plan. What will be Mary’s annual deposit?

b) Mary Hartwell just started her retirement plan. She decided to make equal annual deposits for 30 years. She will then receive payments of $30,000.00 at the end of each of the following 20 years (the first payment will be at t=31). Mary and her insurance company agreed that her account would earn annual interest of 10% for the life of the plan. If Mary deposited $2,250 per year for 30 years, how much could she receive each year for 20 years after she retires?

c) Mary Hartwell just started her retirement plan. She decided to make equal annual deposits for 30 years. She will then receive payments of $30,000.00 at the end of each of the following 20 years (the first payment will be at t=31). Mary and her insurance company agreed that her account would earn annual interest of 10% for the life of the plan. If Mary’s firm decides to contribute an initial $10,000 to her plan now, how much will she have to contribute each year to be able to withdraw $30,000 per year when she retires?

d) Your parents want retirement income of $40,000 per year for 30 years, beginning 21 years from now. They have $20,000 saved so far. How much must they save at the end of each of the next 20 years to meet their goal? The interest rate is 5% compounded annually. Calculate the required annual payment.