Question $3.$

George recently retired at age $70$ and is looking forward to spending retirement with his wife Cloe,

who is $75$ years old. Although both of them are now retired, they would prefer to maintain their

present lifestyle which currently requires annual spending of $75,000$ in real terms. Inflation is

expected to be $6$ percent, and the nominal risk$-$free rate is $10$ percent. The couple's survival

probabilities for the next five years based on their current age are listed in the table below.

a$.$ What is the probability that either George or Cloe will survive over each of the next five

years?

$[5$ marks$]$

b$.$ Is it appropriate to use the expected return of the assets used to fund their spending

needs when calculating the capitalized value of the couple's core capital spending needs?

Why or why not?

$[5$ marks$]$