There is a 50-year-old graduate of UCLA who wants to retire in 20 years at the age of 70. He knows he will die at 90 years old, which is 20 years after he retires. He has no savings and no family. He wants to spend every last penny. He will earn an average of 7% return on his savings for the rest of his 40 years on the planet.

a. he decides he wants his retirement investment fund ("nest egg") to earn $100,000 in each of his 20 retirement years. What should the amount be in his retirement fund ("nest egg") when he is 70? assume all payments are made at the end of each year.

b. He plans to save for his retirement in 20 equal installments from ages 50 - 70 starting at the end of this year. How much should he save annually to build the nest egg calculated above?