Life Insurance Premium Computation

1. Life Insurance Premium Computation • 1. Mortality - 1980 CSO Table (separate tables for male/female) • 2. Interest - time value of money • 3. Loading - for insurer expenses, taxes, profit

2. Commissioners 1980 Standard Ordinary Mortality Table Males Females Deaths Life Deaths Life Age Per 1000 Expectancy Per 1000 Expectancy 30 1.73 43.24 1.35 47.65 31 1.78 42.31 1.40 46.71 32 1.83 40.46 1.45 45.78 33 1.91 39.54 1.50 44.84 34 2.00 38.61 1.58 43.91

3. One Year Term Policy • Alive at age 21 9,810,509 • Number who will die: 10,497 • 1 year term policy without interest: • $10,497,000 9,810,509 = $1.07 • 1 year term policy with interest • $10,497,780 X 0.956994 9,810,509 = $1.02

4. Annual Term for Five Years • Age 21$10,497,780 X 0.956994= $1.02 9,810,509 • Age 22$10,682,000 X 0.95694= $1.04 9,800,012 • Age 23$10,866,000 X 0.95694= $1.06 9,789,330 • Age 24$11,147,000 X 0.95694= $1.09 9,778,464 • Age 25$11,330,000 X 0.95694= $1.11 9,767,317

5. Net Single Premium: 5 Year Term Policy • Amount Present ValueYear Deaths of Claims Discount of Claims • 1 10,497 $10,497,000 0.95694 $10,044,999 • 2 10,682 10,682,000 0.91573 9,781,828 • 3 10,866 10,866,000 0.87630 9,521,876 • 4 11,147 11,147,000 0.83856 9,347,428 • 5 11,330 11,330,000 0.80245 9,091,890 • $47,787,890 • 5 year term net single premium • $47,787,890 9,810,509 = $4.8710

6. Net Single Premium: 5-Year Annuity Due • Present Number Value Age Alive Claims Discount of Claims • 21 9,810,509 $1 due now $1.000 $9,810,509 • 22 9,800,012 $1 due in 1 year 0.95699 9,378,023 • 23 9,789,330 $1 due in 2 years 0.91573 8,694,383 • 24 9,778,464 $1 due in 3 years 0.87630 8,568,868 • 25 9,767,317 $1 due in 4 years 0.83856 8,190,481 • $44,912,264 • 5-year annuity due premium • $44,912,264 9,810,509 = $4.5779

7. Net Single Premium: Whole Life Policy • Amount Present ValueAge Deaths of Claims Discount of Claims • 21 10,497 $10,497,000 0.95694 $10,044,999 • 22 10,682 10,682,000 0.91573 9,781,828 • 23 10,866 10,866,000 0.87630 9,521,876 • ** ***** ****** ***** ***** • 99 30,698 30,698,000 0.03087 947,647 • $1,052,972,752 • Whole Life net single premium • $1,052,972,752 9,810,509 = $107.33

8. Net Level Premium Conversion • $4.5779 is the actuarial equivalent of $1 now and a $1 payment every year for 4 years • Therefore, $4.5779 : $4.8710 = $1 : X • X = $1.064

9. Reserve on Life Insurance Policies • Present Value Present ValueRESERVE = of Future __ of Future Benefits Premiums

10. $1000 Net Single Premium 20-pay life 30-pay life $ 108 Paid-up at 65 Whole life 0 25 35 45 55 65 75 85 95 100

11. Benefit Certain Contracts • Benefit Certain Contracts are those under which, if the insured persists in premium payments, the policy will eventually mature and benefits will be payable. • 1. Cash value policies, under which benefits are payable whether the insured lives or dies are benefit certain contracts. • 2. Ignoring the interest on premiums paid, the net single premium on benefit certain policies equals the face of the policy.

12. Benefit Uncertain Contracts • Benefit uncertain contracts are those under which, if the insured persists in premium payments for the entire policy period, the insurer may or may not be obligated to make payment.