Insurance calculators
Life insurance premium and reserve
Net single premium, net and gross level premiums with expenses, and the net premium reserve for term, whole life, endowment and pure endowment policies.
Inputs
Results
Net single premium
4,631.11
A = 0.01852
Net annual premium
304.57
ä = 15.2053
Gross annual premium
353.80
With expenses
Expense loading
16.2%
Net premium reserve at the start of each year
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Reserves
| Year | Age | Reserve |
|---|---|---|
| 0 | 40 | 0.00 |
| 1 | 41 | 182.00 |
| 2 | 42 | 360.05 |
| 3 | 43 | 532.85 |
| 4 | 44 | 698.94 |
| 5 | 45 | 856.65 |
| 6 | 46 | 1,004.05 |
| 7 | 47 | 1,138.98 |
| 8 | 48 | 1,258.96 |
| 9 | 49 | 1,361.17 |
| 10 | 50 | 1,442.42 |
| 11 | 51 | 1,499.08 |
| 12 | 52 | 1,527.04 |
| 13 | 53 | 1,521.61 |
| 14 | 54 | 1,477.50 |
| 15 | 55 | 1,388.69 |
| 16 | 56 | 1,248.36 |
| 17 | 57 | 1,048.74 |
| 18 | 58 | 781.04 |
| 19 | 59 | 435.25 |
| 20 | 60 | 0.00 |
Methodology
Conventions
- Annual premiums paid in advance while the life is alive, for the premium term. Death benefits are paid at the end of the year of death; endowments at maturity.
- Gross premiums cover an initial expense (a share of the first premium), a renewal expense (a share of each later premium) and a fixed cost per policy each premium year.
- The reserve shown is the net premium (prospective) reserve at the start of each policy year, before that year's premium.
References
- Dickson, Hardy and Waters, Actuarial Mathematics for Life Contingent Risks, 3rd ed.
Formulas
- Term insurance
- A^1_{x:\overline{n}|} = \sum_{k=0}^{n-1} v^{k+1}\,{}_kp_x\,q_{x+k}
- Pure endowment
- {}_nE_x = v^n\,{}_np_x
- Annuity-due
- \ddot a_{x:\overline{h}|} = \sum_{k=0}^{h-1} v^k\,{}_kp_x
- Net premium (equivalence)
- P = S\,A / \ddot a_{x:\overline{h}|}
- Gross premium
- G\ddot a = S A + a\,G + r\,G(\ddot a - 1) + f\,\ddot a
- Net premium reserve
- {}_tV = S\,A_{x+t} - P\,\ddot a_{x+t:\overline{h-t}|}