Assume that your mother is now 58 years old, that she plans to retire in 12 years, and that she expects to live for 25 years after she retires. She wants her first retirement payment to have the same purchasing power at the time she retires as $50,000 has today. Inflation is expected to be 3% per year from today forward. She wants all of her subsequent retirement payments to be equal to her first retirement payment (i.e., do not let the payments after retirement grow with inflationnot realistic!). Her retirement income will begin the day she retires, 12 years from today, and she will then receive 24 additional annual payments, for a total of 25 annual payments (hint: annuity due will help here!). During retirement, her conservatively-invested portfolio will earn 4% per year. She currently has $150,000 saved, and she expects to earn a return on her savings of 8% per year with annual compounding between now and retirement.

a) To the nearest dollar, how much will she need to have each year in retirement in nominal dollars? In other words, what is $50,000 today equal to at the time she retires?

b) To the nearest dollar, how much will she need to have saved at the date of retirement to support this planned income stream?

c) To the nearest dollar, how much must she save during each of the next 12 years (with equal deposits being made at the end of each year, beginning a year from today) to meet her retirement goal?