Why is the return so much lower than the gain suggests?

Because the gain ignores time. Getting ₹7,00,000 more than you paid sounds large, but the first premium was committed twenty years earlier. Spreading the growth across those years is what turns a big-looking total into a single-digit annual rate.

Is a policy with a lower return a bad policy?

That is not a question arithmetic can answer, and this site does not answer it. A savings policy bundles cover with saving; the rate here prices the saving half only. What the calculator does is stop the rate being invisible.

What rate should I compare against?

Whatever you would genuinely have done with the money, at a return you would genuinely have accepted. The field is yours to set, and trying a range is more informative than any single number.

Why do premiums count from the start of the year?

Because that is when an insurer takes them. Treating a premium as paid at the end of the year would shorten the time it is invested and flatter the resulting rate.

Insurance Policy Return Calculator

An endowment or savings policy is sold on two numbers: the premium and the maturity amount. Neither tells you the rate of return, and the rate is the only figure that lets you compare the policy with anything else. This solves for it from the premiums you pay and the amount you are shown.

Check the working

A worked example

A fixed case, for reference.

₹50,000 a year for ten years, on a policy that matures in the twentieth year paying ₹12,00,000.

Premiums paid
$50000 \times 10 = 5{,}00{,}000$
Received over premiums paid
$1200000 - 500000 = 7{,}00{,}000$
The rate that clears the cashflows
$\approx 5.7\% \text{ a year}$

The policy pays back ₹7,00,000 more than went in — a figure that looks large and says nothing on its own. As an annual rate over the twenty years the money is committed, it is about 5.7%. Whether that is acceptable depends on what else you would have done with the premiums, and on the value of the life cover the policy also carries, which this calculation does not measure.

The formula

0 = \sum_{t=0}^{p-1} \frac{-P}{(1 + r)^{t}} + \frac{M}{(1 + r)^{n}}

The rate r at which every premium paid, and the maturity amount received, discount back to nothing between them. That rate is the policy’s return.

What each symbol means

P: the premium paid at the start of each paying year
p: the number of years premiums are paid
M: the amount received at maturity
n: years from the first premium to maturity
r: the annual return being solved for

What this assumes, and where it stops

Assumptions

Premiums are paid annually, at the start of each paying year, with none missed.
The maturity amount is received as a single payment at the end of the term.
The amount you enter is what you actually receive. Illustrations often mix a guaranteed amount with a projected bonus — enter the guaranteed part if you want the rate you are certain of.
The comparison rate is your own assumption, applied to the same premiums on the same dates.

Limitations

Life cover is not valued. A savings policy pays out on death as well as at maturity, and that has a worth this calculation says nothing about.
Money-back policies that pay survival benefits during the term are not modelled, nor are unit-linked plans whose value moves with markets.
Bonuses that are declared rather than guaranteed cannot be known in advance, so a rate computed from a projected maturity amount is a projection too.
Tax is not modelled, on either the premiums or the payout.
Surrender before maturity is not modelled, and surrender values are typically far below premiums paid in the early years.

What this calculator does

Finds the annual rate at which your premiums grow into the maturity amount, counting when each premium is paid.
Separates the cash gain — maturity amount minus premiums paid — from the rate, which are very different things over twenty years.
Compounds the identical premiums at a rate you choose, so the comparison is against your own assumption rather than one this site picked.
Handles policies where premiums stop before maturity, which is how most are structured.

Common questions

Different questions about the same money. These use the same conventions, so the numbers are comparable.

XIRR Calculator
Calculate the annualised return on irregular cashflows — the right measure when money went in and out on different dates.
PPF Calculator
Project a Public Provident Fund balance under the scheme’s own rule — interest on the lowest balance between the 5th and month-end — and see what missing that date costs.
SIP Calculator
Project what a monthly SIP could grow to over time, and see how much of the total is your own contribution versus assumed returns.
Investment Goal Calculator
Start from the amount you want and work backwards to the monthly investment it would take to get there.