Calculator Inputs
Choose a product mode, set mortality and discount assumptions, then calculate the actuarial present value.
Formula Used
Periodic interest conversion: ip = (1 + i)1/m - 1
Periodic mortality conversion: qp = 1 - (1 - q)1/m
Periodic survival probability: pp = 1 - qp
Discount factor: v = 1 / (1 + ip)
Temporary annuity immediate: APV = Σ [Bk × ppD+k × vD+k]
Temporary annuity due: APV = Σ [Bk × ppD+k × vD+k] with the first payment at the beginning of each period.
Term insurance: APV = Σ [Bk × ppD+k-1 × qp × vD+k]
Pure endowment: APV = M × ppD+N × vD+N
Endowment insurance: APV = term insurance component + pure endowment component
Loaded APV: Loaded APV = Net APV + (Net APV × expense loading) + flat expense
Here, m is payments per year, D is deferred periods, N is benefit periods, Bk is the period benefit, and M is the maturity benefit.
How to Use This Calculator
- Choose the actuarial product type that matches your valuation problem.
- Enter current age, terminal age, and the benefit term.
- Set the annual effective interest rate and annual mortality rate.
- Enter the payment or death benefit amount. Add a maturity benefit when relevant.
- Select annual, semiannual, quarterly, or monthly valuation frequency.
- Add growth, deferral, and expense assumptions for a more realistic estimate.
- Click Calculate APV to see the result above the form.
- Review the valuation schedule, then export the output to CSV or PDF if needed.
Example Data Table
These examples use the same formulas implemented in the calculator and show illustrative present values.
| Scenario | Product | Age | Term | Interest % | Mortality % | Frequency | Benefit | Maturity Benefit | Net APV | Loaded APV |
|---|---|---|---|---|---|---|---|---|---|---|
| Level term insurance | Term Insurance | 40 | 15 | 4.5 | 1 | 1 | 150,000.00 | 0.00 | 15,152.46 | 15,727.04 |
| Growing annuity due | Temporary Life Annuity Due | 50 | 10 | 5 | 0.8 | 12 | 12,000.00 | 0.00 | 1,075,887.31 | 1,097,480.06 |
| Endowment insurance | Endowment Insurance | 35 | 20 | 5 | 1.2 | 1 | 100,000.00 | 50,000.00 | 28,427.08 | 30,098.44 |
Frequency codes: 1 = annual, 2 = semiannual, 4 = quarterly, 12 = monthly.
FAQs
1. What does actuarial present value measure?
Actuarial present value measures the discounted expected value of future contingent cash flows. It combines time value of money with survival or death probabilities under the chosen assumptions.
2. Why does payment frequency change the result?
Changing frequency changes the timing of benefits, discounting intervals, and converted mortality per period. Monthly or quarterly cash flows usually produce a different present value than annual cash flows.
3. What is the difference between annuity immediate and annuity due?
Annuity immediate assumes payments occur at the end of each period. Annuity due assumes payments occur at the beginning of each period, which generally increases the present value.
4. How is mortality handled in this calculator?
The calculator uses a constant annual mortality rate and converts it to the selected payment period. That makes the model practical for estimation, sensitivity testing, and educational comparisons.
5. When should I use a pure endowment calculation?
Use a pure endowment when the benefit is paid only if the person survives to a specified future date. There is no death benefit during the term.
6. What does loaded APV include?
Loaded APV adds expense allowances to the net actuarial present value. This version includes a percentage loading on net APV and a separate flat expense amount.
7. Why is terminal age needed for whole life modes?
The terminal age creates a practical projection horizon. It prevents an infinite schedule and lets the calculator estimate whole life values using a finite actuarial approximation.
8. Can I use this for pricing or reserves?
It is useful for educational work, quick modelling, and sensitivity checks. Formal pricing and reserves usually require detailed mortality tables, expenses by duration, and regulatory methods.