What is a reversionary bonus?

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asked Nov 8, 2017

The following is an extract from the DHW textbook:

"Exercise 6.8

Consider an annual premium with-profit whole life insurance
issued to a select life aged exactly 40. The basic sum insured is $200 000 payable at the end of the month of death, and the premium term is 25 years. Assume a compound reversionary bonus of 1.5% per year, vesting on each policy anniversary, initial expenses of 60% of the annual premium, renewal expenses of 2.5% of all premiums after the first, plus per policy expenses (incurred when a premium is payable) of$5 at the beginning of the first year,
increasing by 6% per year compound at the beginning of each subsequent year.
Calculate the annual premium."

Please could someone explain what a compound reversionary bonus is and how it will be treated in this question.

1 Answer

+1 vote
answered Nov 11, 2017 by (2,200 points)

With-profit contracts are life insurance policies where the sum assured is increased by distributing a portion of the surplus generated throughout the term of the contract to policyholders. This distributed surplus is called a bonus (the surplus distributed to shareholders is called a dividend). This bonus can be distributed on a regular basis, say annually, which we term a reversionary bonus or at the end of the contract, called a terminal bonus.

A compound reversionary bonus is calculated as a percentage of the sum assured and all previously accrued bonuses. This means that the bonus of each year is added to the sum assured and the bonus  for the following year is calculated on this (new) enhanced sum assured.

In the context of this question, the compound reversionary bonus will affect the sum assured of the contract in the following way:

 year (t) sum assured in year (t) bonus at end of year (t) 1 $$200000$$ $$200000 \times 1.5\% = 3000$$ 2 $$203000$$ $$203000 \times 1.5\% = 3045$$ ... ... ... 10 $$228678$$ $$228678 \times 1.5\% = 3430$$

In other words, the sum assured in year t = $$200000 \times (1.015)^{t-1}$$