Joe, age $65,$ recently retired after a long career in the aerospace industry, first as a pilot, then as a test

pilot, and finally as a project manager overseeing the testing and production of planes. He and his wife

Charlene, age $63,$ recently retired. Even though they are retired, they prefer to maintain their current

lifestyle with spending needs of $$80,000$ per year in real terms. Inflation is expected to be $3\%$ with the

nominal risk$-$free rate equal to $5\%.$ The couple's survival probabilities for the next three years are shown

in the table below.

A$.$ Determine the probability that either Joe or Charlene will survive for three years.

B$.$ Calculate the capitalized value of the couple's core spending needs over the next three years.

To calculate core capital for an individual, you would:

A$.$ forecast future nominal needs, discount at the real risk$-$free rate, and then add a safety reserve.

B$.$ forecast future real needs, discount at the real risk$-$free rate, and then subtract a safety reserve.

C$.$ use Monte Carlo simulation to project how long existing capital is projected to last.