A person's $500,000 life assurance benefit is to be invested at j₂=6.5% p.a. with semi-annual payments of $20,000, beginning immediately, made to the surviving spouse for life. On the payment date immediately following the spouse's death, the remainder is to be gifted to the Red Cross.

1. Draw a correct timeline with the information provided.
2. If the spouse lives for a further six years, six months, how much would the Red Cross receive?
3. How would your answer above (in b)) change if the interest rate was compounded quarterly j₄?
4. Managers of a superannuation scheme, with no spouse benefits, estimate that 80% of members will live long enough to collect some benefits. If the age distribution of members at death is about normal with a mean of 82 years, and a standard deviation of 5 years, what is the age at which people can begin collecting?