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Xavier (aged 45) would like to buy a reversionary annuity with a single premium payable today for his brother Yusuf (aged 41). On the death of Xavier, the annuity will make payments monthly in arrears for as long as Yusuf is alive. Xavier has $200,000 to spend on this annuity.

Basis: AM92 Ultimate, Interest 4% p.a.
Profit loading: 3% of each annuity payment
You are given that ä 15:41 = 17.577
a) What is the monthly annuity payment that this premium would buy?
b) Ten years later, Xavier has died and Yusuf is still alive. What is the policy value at this time if future profits are not allowed for?
c) Suppose instead of paying for this annuity with a single lump sum, Xavier and Yusuf would like to pay a level premium annually in advance. Determine a suitable premium term and calculate the annual premium.


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