Free SOA Exam ALTAM (Advanced Long-Term Actuarial Mathematics) Pension Plans and Retirement Benefits Practice Questions

D is correct.

The replacement ratio measures post-retirement income as a fraction of pre-retirement income. Financial planning guidelines commonly target approximately 70% to 85% because retirees typically face: (1) lower income taxes (reduced taxable income and no payroll taxes on earnings); (2) elimination of work-related expenses such as commuting, work clothing, and meals away from home; and (3) no further need to set aside savings for retirement. Because these outflows disappear at retirement, a retiree needs less gross income than during working years to sustain a comparable standard of living, so a target below 100% is adequate rather than deficient.

E is correct.

For a final average pay plan where salaries are expected to grow:

- **Unit Credit (UC):** the accrued benefit uses current salary only (not projected), so the AAL is the present value of a benefit based on today's salary, the lowest of the three.
- **Entry Age Normal (EAN):** costs are spread as a level amount or percentage from entry age to retirement based on the projected final benefit; the AAL at mid-career reflects accumulated level contributions, producing a moderate AAL.
- **Projected Unit Credit (PUC):** the accrued benefit uses projected final salary (the full projected benefit prorated by service to date), so the AAL at mid-career is the present value of a benefit reflecting projected salary growth, the highest of the three.

Therefore: $\text{AAL}_{\text{UC}} \leq \text{AAL}_{\text{EAN}} \leq \text{AAL}_{\text{PUC}}$.

C is correct.

Let $S_0$ be the current salary. End-of-year contributions are $c \cdot S_k = c \cdot S_0 (1.03)^k$ for $k = 1, \ldots, 30$. The accumulated fund at retirement is: $$F = c S_0 \sum_{k=1}^{30} (1.03)^k (1.07)^{30-k} = c S_0 (1.07)^{30} \sum_{k=1}^{30} \left(\frac{1.03}{1.07}\right)^k$$ Factoring out the salary growth gives $$F = c S_0 (1.03)^{30} \cdot s_{\overline{30}|g}, \qquad g = \frac{1.07}{1.03} - 1 \approx 0.0388.$$ The target fund is $0.70 \times S_{30} \times 13 = 0.70 \times S_0 (1.03)^{30} \times 13$. Setting the two expressions equal, the factor $S_0 (1.03)^{30}$ cancels from both sides and $$c = \frac{0.70}{13 \cdot s_{\overline{30}|g}}, \quad g \approx 0.0388.$$ The annuity factor 13 sits in the denominator: a larger factor (more expensive income) is offset by a target fund that buys the same 70% of final salary, and the accumulation uses the excess of investment return over salary growth rather than the raw 7%.