1. The analysis of the surplus of a life office disclosed by a bonus reserve valuation does not differ in principle from the analysis of the results of a valuation on a net premium basis, but the treatment of bonus requires special consideration. A method of analysis appropriate to a uniform compound reversionary bonus is discussed in the following paragraphs, and a numerical example is given by way of illustration.

2. It is assumed that the valuation formula is

where (S + B) represents the sum assured and existing bonuses,

P is the office premium,

k is the proportion of premium reserved for expenses,

x is the present age nearest birthday,

n is the curtate duration to maturity,

b is the rate of bonus for which a specific reserve is made.