In discrete summations for varying insurance, what does the term 'kurtate' signify about the indexing of years?

• A. The first year is indexed as k = 0
• B. The first year is indexed as k = 1
• C. The last year is indexed as k = n
• D. Time is treated continuously

Answer: (A)

In curtate (kurtate) time, time is counted in whole years starting from zero. That means k counts the number of completed years since the policy begins, so the first year is labeled with k = 0. For a term of n years, the usual indexing runs from k = 0 up to k = n−1, reflecting one term for each completed year while keeping the start at time zero. This is distinct from continuous-time modeling, which uses non-integer time generally, and from indexing that starts at k = 1. So the first year is indexed as k = 0.