If policy value at time t is part of the death benefit at t and equivalence is not explicitly stated, which formula is commonly used to relate benefits and policy values?

• A. (tV + P)(1+i) = bqx + t+sVpx
• B. tV = P + bqx
• C. V = iP + bqx
• D. (V + P)(1+i) = bqx + tVx

Answer: (A)

The idea being tested is how to relate the policy’s cash value to the death benefit when the cash value is included in what’s payable, accounting for the time value of money. If the policy value at time t is being carried into the death benefit, you balance resources by accumulating the currently available amount forward and equating it to what must be paid out or continued in the future.

Concretely, take the cash value at time t and any new premium P, and accumulate that sum to the next evaluation point at rate i. That accumulated amount must cover both the death benefit payable now (or in the near term) and the value of continuing the policy to a future point, which is represented by the future value term t+sVpx. Thus the left-hand side, (tV + P) grown at rate i, equals the right-hand side, the death benefit bqx plus the future value of the policy t+sVpx.

This formulation is the standard way to link benefits and policy values when the policy value is part of the death benefit and no explicit equivalence is stated. The other forms fail to properly reflect the forward accumulation of the current value and premium or misplace the timing of the values being equated.