Q.Using the same table (l₃₁ = 99,800; d₃₁ = 220), find the rate of mortality and the one-year natural premium at age 31 for a sum assured of Rs 1,000 (ignore interest and expenses). State whether the premium is higher or lower than at age 30, and why.

Because mortality rises with age, the natural premium at 31 should come out slightly higher than at 30.

Step 1 — Rate of mortality at age 31.

q₃₁ = d₃₁ ÷ l₃₁ = 220 ÷ 99,800 = 0.0022044… ≈ 0.002204.

Step 2 — Natural premium at age 31.

Natural premium = q₃₁ × sum assured = 0.002204 × Rs 1,000 = Rs 2.204 ≈ Rs 2.20.

Check (dual-solve). Fund if all 99,800 lives pay Rs 2.204 each = 99,800 × 2.204 = Rs 2,19,959 ≈ Rs 2,20,000. Expected claims = 220 deaths × Rs 1,000 = Rs 2,20,000. The fund matches the claims, confirming the premium.

Step 3 — Comparison with age 30. …

Rounding too early (e.g. taking q as 0.002 and getting exactly Rs 2.00) hides the increase — carry enough decimals. Some students wrongly expect the premium to fall becau …