Most people believe life insurance premiums are decided simply by age, smoking habits or medical reports. This data is considered, but every premium is backed by mathematics, probability, statistics, finance and actuarial science. Every life insurance company must answer one fundamental question before issuing a policy.

“What is the probability that this individual will die during the policy term?”
The answer isn’t based on guesswork. It is calculated using Mortality Table, Makeham’s Law of Mortality, Probability Theory, Present Value mathematics and Insurance reserving. This article will explain in brief the actuarial process in simple language. 

Why do Insurance Companies Need Mathematics?
Imagine 1,00,000 people buying a Rs 1 Crore term insurance policy. The insurer would have to pay Rs 1,00,000 Crore in case of claim, if all individuals were to perish tomorrow but obviously, this does not happen. Only a very small percentage die every year. The insurer’s entire business depends on predicting that percentage as accurately as possible. That prediction begins with “Mortality Tables.”

What is a Mortality Table?
A mortality table (also called as a life table) is a statistical database showing the probability of death at every age. Instead of guessing, actuaries study historical records and determine,

·       How many people survive to age 25?

·       How many people survive to age 40?

·       How many will survive to age 60?

·       How many will die before their next birthday?

These probabilities become the foundation of life insurance pricing. In India, insurers commonly rely on mortality investigations as the Indian Assured Lives Mortality (IALM) table, along with their own experience and regulatory assumptions.

Why can’t companies use Raw Mortality Data?
Historical data contains random fluctuations, for example, one particular year may witness

·       Pandemic,

·       Floods

·       Earthquake

·       Wars

These events distort the data. Instead of using irregular figures directly, actuaries smooth the data using mathematical models. The most famous of these is “Makeham’s Law of Mortality.”

Understanding Makeham’s Law
Mr Benjamin Gompertz observed that as humans age, their probability of dying increases exponentially. William Makeham improved this concept by adding another important factor. Even young healthy individuals die because of

·       Road Accidents

·       Natural Disasters

·       Aviation Accidents

·       Fire

·       Other unpredictable events

This constant accidental risk was added to Gompertz’s equation and the final formula became “Force of Mortality” as follows 

u_(x) = A+[B*(C^x)]

Where,

Standard illustrative values, that many actuarial textbooks use for illustrative assumptions are as follows

These values help students understand the mathematics behind premium calculations. Actual assumptions used by insurers vary depending on product design, mortality experience, investment assumptions, expenses and regulatory requirements.

Let’s take an example,

Step 1 – Calculate Force of Mortality

Current Age = 25 Years,

By using Force of Mortality formula, u_(x) = A+[B*(C^X)]

A = 0.0007

B = 0.0001

C = 1.085

Age (x)= 25

Calculations

u_(25) = 0.0007+[0.0001*(1.085^25 )]

u_(25) = 0.0014684

This represents the instantaneous force of mortality at age 25, under these illustrative assumptions.

Step 2 – Calculating Cumulative Mortality

Suppose a person buys a 40-year term insurance plan at age 25. The insurer will then calculate mortality for every single age. Instead of calculating mortality separately, actuaries sum them using summation

∑_25^64 [u_(x)]

So, the illustrative calculation looks as follows

0.0007*40 = 0.028

0.0001* [ ∑_25^64 (1.085) ^x] = 0.22725

0.028 + 0.22725 = 0.25525

Step 3 – Calculating Survival Probability

Once cumulative mortality is known, survival probability becomes

P = e^(-0.25525)

P = 0.77472

Meaning, there is approximately a 77.47% probability of surviving from age 25 to age 65 under this illustrative model.

Step 4 – Calculating Death Probability

Since, SURVIVAL + DEATH = 100%, Death probability

1 - 0.77472 = 0.22528

22.53%

The insurer therefore estimates an illustrative 22.53% probability that the claim may arise during the policy term.

Premium Calculations don’t stop here
Many people believe this probability directly becomes the premium. It doesn’t. The insurer must still account for several additional factors before deciding the final premium amount, such as

·       Mortality risk

·       Interest earnings

·       Policy administration expense

·       Distribution commissions

·       Taxes

·       Stamp duty

·       Reinsurance costs

·       Profit margins

·       Solvency requirements

·       Office & staff expenses

·       Other expenses

This is where actuarial pricing becomes much more sophisticated.

Understanding Insurance Reserving
Imagine 10,000 people, each purchasing Rs 1 Crore Term insurance. The insurer immediately receives premiums. Can it spend all the money? No.

A large portion must be kept aside as policy reserves to ensure future claims can be paid, even many years later. Reserving is one of the most important responsibilities of an actuary because it protects the insurer’s long-term financial stability and supports regulatory solvency requirements.

Why Interest Rate Matters?
Premiums collected today are invested until future claims arise. Actuaries therefore discount future liabilities to their Present Value (P.V). This basic concept works on the following formula,

P.V = (F.V) / [(1+i)^n]

Where,

·       P.V = Present Value

·       F.V = Future Value

·       i = Interest Rate

·       n = Number of years

For example,

Future Claim = Rs 1 Crore

Interest Rate = 6%

Claim after 40 years

P.V = 1,00,00,000 / [(1.06)^40]

This demonstrates why investment returns are a key component of premium pricing.

Why Younger People Pay Lower Premiums

A 25-year-old has

·       Lower mortality risk

·       Longer investment horizon

·       More years to pay premiums

·       Lower expected claim probability during policy term

As age increases,

·       Mortality rises

·       Remaining premium-payment years reduce

·       Probability of claim increases

·       Required reserves increase

This is why premiums generally increase with entry age.

What this Means for Policy Holders?
Understanding the mathematics behind life insurance helps you appreciate why insurers ask detailed questions about your age, health, occupation and lifestyle. These details are not collected to complicate the buying process, they actually help actuaries estimate risks, calculate fair premiums and ensure that insurers remain financially capable of paying future claims.

INSURANCE AWARENESS > INSURANCE IGNORANCE

Helping individuals and families make informed insurance decisions through education, transparency, and awareness.

Last Updated – 22/06/2026
Author Name - Abhishek Borkar

Disclaimer
This article is intended solely for educational and awareness purposes and should not be considered financial, legal, tax, investment, or insurance advice.

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