Free SOA Exam ALTAM (Advanced Long-Term Actuarial Mathematics) Universal Life Insurance Practice Questions

B is correct. A universal life policy lapses when the account value is reduced to zero or below after charges are applied and the policyholder fails to make a sufficient premium payment within the grace period (typically 61 days) to restore a positive account value. This is the defining feature of UL's flexible premium structure: the policy persists only as long as the account value is sufficient to cover ongoing COI and expense charges.

A is incorrect: the guaranteed minimum credited rate is a contractual floor; if the insurer fails to credit at least that rate, it is a contract breach — not a lapse trigger. The credited rate falling below the guarantee is an insurer obligation problem, not a policyholder lapse event.
C is incorrect: switching between death benefit options is a policyholder right under the contract and does not cause lapse; no new underwriting is required.
C is incorrect: the NAR exceeding the face amount is definitionally impossible under standard Type A (NAR = DB − AV < DB for positive AV) and under Type B the NAR always equals the face amount.
E is incorrect: expense charges exceeding the monthly premium deplete account value but do not independently trigger lapse without the account value actually reaching zero.

B is correct. Under a Type A (level death benefit) policy, the death benefit is fixed at the face amount. As the account value grows, the net amount at risk (NAR = death benefit - account value) shrinks:

$$\text{NAR}_A = \text{Face Amount} - \text{AV} \quad (\text{decreases as AV grows})$$

Under a Type B (increasing death benefit) policy, the death benefit equals face amount plus account value, so the NAR is always the face amount:

$$\text{NAR}_B = (\text{Face Amount} + \text{AV}) - \text{AV} = \text{Face Amount} \quad (\text{constant})$$

This means COI charges under Type B are higher and more stable over time, while Type A COI charges decline as the account value grows.

Why each other option is incorrect:
- (B) While COI rates rise with age, the NAR under Type A still decreases because the account value growth (reducing NAR) typically outpaces the age-driven rate increase. Under Type B, the NAR is constant at the face amount, not decreasing.
- (C) The NAR decreases under Type A but stays constant under Type B; they do not both decrease.
- (D) Under Type A, the NAR equals face amount minus account value (not always equal to face amount); once the account value reaches the face amount, the NAR approaches zero. The self-insurance characterization of Type A is incorrect.
- (E) Under Type A, the NAR is not fixed at the face amount; it equals face amount minus account value and declines. Under Type B, the NAR equals the face amount (not the account value).

D is correct. Compute discounted profits at 10%: Year 1: $-800/1.10 = -727.27$. Year 2: $100/1.21 = 82.64$. Year 3: $200/1.331 = 150.26$. Year 4: $350/1.4641 = 239.06$. Year 5: $500/1.61051 = 310.46$. Cumulative: After year 1: $-727.27$. After year 2: $-644.63$. After year 3: $-494.37$. After year 4: $-255.31$. After year 5: $-255.31 + 310.46 = 55.15 > 0$. The cumulative first becomes non-negative at the end of year 5; therefore, DPP = 5. Option A claims DPP = 2, which is too early. Option B claims DPP = 3, also too early. Option C correctly computes the year-4 cumulative as -255.3 but then incorrectly concludes payback occurs at year 4. Option D raises a valid technical point but the question provides the profit signature and asks for the DPP directly from these figures.