Calculator inputs
Example data table
| Scenario | Policy Type | Entry Age | Term | Death Benefit | Maturity Benefit | Interest % | Initial qx % | Mortality Growth % |
|---|---|---|---|---|---|---|---|---|
| Example A | Endowment Assurance | 35 | 20 | 100,000 | 100,000 | 4.50 | 0.35 | 6.00 |
| Example B | Term Insurance | 42 | 15 | 250,000 | 0 | 5.20 | 0.60 | 5.00 |
| Example C | Pure Endowment | 28 | 25 | 0 | 150,000 | 4.00 | 0.22 | 4.20 |
Formula used
Net single premium is the expected present value of future benefits only. It excludes expenses, profit margins, and policy fees.
Discount factor: \( v = \frac{1}{1+i} \)
Projected mortality: \( q_{x+t} = \min\bigl(0.999999,\; q_x(1+g)^t \bigr) \)
Survival to year start: \( {}_tp_x = \prod_{k=0}^{t-1}(1-q_{x+k}) \)
Term or whole life death benefit: \( NSP = S \sum_{t=0}^{n-1} v^{t+\delta}\,{}_tp_x\,q_{x+t} \)
Pure endowment: \( NSP = M \cdot v^n \cdot {}_np_x \)
Endowment assurance: \( NSP = \text{Death EPV} + \text{Maturity EPV} \)
Timing rule: \( \delta = 1 \) for end-of-year payments and \( \delta = 0.5 \) for a mid-year approximation.
How to use this calculator
- Choose the policy type that matches the benefit design.
- Enter the issue age and, when needed, the policy term.
- Input death benefit, maturity benefit, interest rate, and mortality assumptions.
- Choose whether death claims are discounted to year-end or mid-year.
- Click the calculate button to show the premium above the form.
- Review the summary, projection table, and Plotly graph.
- Download the schedule as CSV or PDF for documentation.
FAQs
1) What does net single premium mean?
It is the present value of expected policy benefits, paid once upfront. It ignores expenses, commissions, taxes, and profit loadings.
2) Why is mortality so important here?
Mortality controls the probability and timing of claims. Higher death probabilities usually raise death-benefit present value and can reduce survival benefits.
3) What is the difference between term and endowment?
Term insurance pays only on death during the term. Endowment assurance pays on death during the term or on survival to maturity.
4) Why can a higher interest rate reduce the premium?
A higher discount rate lowers present values. Future benefits are discounted more strongly, so the single premium often becomes smaller.
5) When should I use mid-year payment timing?
Use it when death claims are assumed to occur evenly through the year. It gives slightly less discounting than end-of-year payment timing.
6) What does the maximum valuation age do?
It limits the projection horizon. Whole life coverage is approximated by valuing death benefits until that maximum age is reached.
7) Can this replace a full actuarial valuation?
No. It is an educational and planning calculator. Real pricing often uses detailed life tables, decrements, expenses, reserves, and regulation-specific rules.
8) Why does pure endowment ignore the death benefit?
Pure endowment pays only if the insured survives to the end of the term. No death benefit is valued in that structure.