Actuarial Table B Calculator

Calculator Inputs

Enter age, discount rate, payment value, mortality adjustments, and payment timing. Optional custom mortality data can replace the sample curve.

Current age

Starting age for the life table projection.

Limiting age

Projection cannot pass this age.

Term in years

Use a term, or set it near the limiting age.

Annual interest rate (%)

Effective annual discount rate.

Annual payout or principal

Used for annuity, insurance, and endowment values.

Payment frequency

Payment is divided across the year.

Payment timing

Immediate pays at period end. Due pays at period start.

Death benefit timing

Choose how death payments are discounted.

Mortality adjustment (%)

Positive values increase mortality rates.

Age adjustment

Use negative for age setback, positive for rating up.

Mortality improvement (%)

Annual reduction applied to future q values.

Custom mortality table

Optional. Enter one age and q value per line.

Example Data Table

This sample shows default mortality and one-year present value logic at a 4% interest rate.

Age	q_x	p_x	One-Year Discount	Death Benefit PV Factor
40	0.001169	0.998831	0.961538	0.001124
50	0.002850	0.997150	0.961538	0.002740
60	0.006681	0.993319	0.961538	0.006424
70	0.016759	0.983241	0.961538	0.016114
80	0.040282	0.959718	0.961538	0.038733

Formula Used

Survival: p(x,t) = Π(1 - qx+k)

Discount: v^t = (1 + i)^-t

Annuity factor: a = Σ p(x,t) × v^t / m, where m is payment frequency.

Insurance factor: A = Σ p(x,k) × qx+k × v^(k+payment time)

Pure endowment: E = p(x,n) × v^n

Income-interest factor: I = i × ä. The remainder estimate is 1 - I.

How to Use This Calculator

Enter the current age and the term you want to test.
Add an annual interest rate and the payout or principal amount.
Choose payment frequency and timing.
Adjust mortality by percentage, age rating, or improvement rate if needed.
Paste custom age and q values if you have your own table.
Press the calculate button to show results above the form.
Use the CSV or PDF buttons to export the summary and projection.

Actuarial Table B Calculator Guide

Purpose of the Tool

An actuarial table connects age, mortality, interest, and time. This calculator turns those ideas into practical factors. It helps you estimate annuity values, life insurance values, survival chances, and remainder values from one clear input panel. The tool is built for learning, checking assignments, and comparing assumptions before using formal tables.

Why Mortality Matters

The key input is qx. It means the chance that a person aged x dies before the next birthday. A lower qx increases expected payments that depend on survival. A higher qx increases death benefit values. The calculator includes a sample mortality curve, but you can paste your own age and qx data for more specific work.

Interest and Present Value

Future payments are not valued at their face amount today. They are discounted by the interest rate. A higher rate reduces present value because distant payments become worth less. This is why the same payout can produce different factors when the discount rate changes.

Annuity and Benefit Factors

The annuity factor measures the present value of expected survival payments. You can select immediate or due timing. Immediate payments occur at period ends. Due payments occur at period starts. Death benefits can be discounted at the middle or end of each year, which changes the insurance factor slightly.

Useful Comparisons

Use the result table to inspect each projection year. It shows qx, px, survival, death probability, annuity contribution, and insurance contribution. These rows make the final numbers easier to audit. They also show which ages drive most value.

Exporting Results

CSV export is useful when you want to review assumptions in a spreadsheet. PDF export is useful when you need a quick summary for notes, teaching, or review. Because the projection rows are visible, you can trace each factor instead of accepting a black box answer during later study reviews.

Important Caution

This tool is not a substitute for official tables. Pension plans, tax filings, court matters, and estate calculations may require prescribed rates and published mortality tables. Always verify those requirements before relying on an estimate. For study, planning, and model testing, the calculator gives a fast and transparent starting point.

FAQs

What does qx mean?

qx is the probability that a person aged x dies before reaching age x plus one. It is one of the main mortality inputs in actuarial calculations.

What is px in the result table?

px is the one-year survival probability. It equals one minus qx. The calculator uses it to build multi-year survival probabilities.

What is an annuity factor?

An annuity factor is the present value of one expected annual payment stream. Multiplying it by the payout gives the estimated annuity value.

What is the insurance factor?

The insurance factor estimates the present value of a death benefit. It combines survival to each year, death probability, and discounting.

Can I use my own mortality table?

Yes. Paste rows in age,qx format. The calculator will use your entered ages where available and use the sample curve for missing ages.

What does age adjustment do?

Age adjustment changes the effective age used for mortality lookup. A positive value raises mortality. A negative value lowers it.

Why does payment timing matter?

Payments made earlier are discounted less. Annuity due values are usually higher than immediate values when all other inputs stay equal.

Is this an official actuarial table?

No. It is an educational calculator with a sample curve and custom table support. Always use prescribed official data for regulated work.