The natural premium is just the probability of death multiplied by the sum assured, so the mortality table gives everything needed.

Ignoring interest and expenses, each life must contribute exactly its chance of dying times the sum assured, so the total collected meets the expected claims.

Step 1 — Rate of mortality at age 30.

The rate of mortality qₓ = dₓ ÷ lₓ.

Here d₃₀ = 200 and l₃₀ = 1,00,000, so

q₃₀ = 200 ÷ 1,00,000 = 0.002, i.e. 2 deaths per thousand lives.

Step 2 — Natural (risk) premium for one year.

Ignoring interest and expenses, the pure premium each life must pay for one year's cover equals the rate of mortality × sum assured, because the total so collected exactly meets the expected claims of those who die during the year.

Natural premium = q₃₀ × sum assured = 0.002 × Rs 1,000 = Rs 2.00.

Check (dual-solve). If all 1,00,000 lives each pay Rs 2, the fund collected = 1,00,000 × Rs 2 = Rs 2,00,000. The claims to be paid = 200 deaths × Rs 1,000 = Rs 2,00,000. The fund exactly equals the claims, confirming the premium of Rs 2.00 is correct.

Alternative view: total expected claims (200 × Rs 1,000 = Rs 2,00,000) divided equally among all 1,00,000 living lives gives Rs 2,00,000 ÷ 1,00,000 = Rs 2.00 each — the same natural premium, reached from the fund side rather than the probability side.

A frequent error is dividing by dₓ instead of lₓ, or forgetting to multiply the probability by the sum assured. Another is adding interest/loading when the question says to ignore them — read the question's assumptions.