In discrete annuities, which probability appears in place of k|qx in the formulation for varying insurance?

• A. tpx
• B. qx
• C. px
• D. tqx

Answer: (A)

In discrete time for varying insurance, each payment is made if the insured is alive at the corresponding payment time. So the weight you use for a payment at time t is the probability of surviving to that time, which is tpx (the life aged x surviving t years). This is why tpx appears in the formulation: it directly corresponds to the chance the benefit is actually paid at each date.

Other options don’t capture this survival-or-not condition. qx is the one-year probability of dying, not survival to a future date; px is the probability of surviving one year (not a vector of survival to successive years); tqx isn’t the standard survival weight used across multiple future times.