Immediate annuity payout calculator

What is an immediate annuity payout calculator?

An immediate annuity payout calculator tells you how much income a lump sum will pay you each period, for a fixed number of periods, once you convert that sum into an annuity. You hand an insurer or a plan a single principal (often called the premium), and in return it pays you a level amount every month, quarter, or year until the term ends. The tool answers the practical question at the heart of that trade: for this principal, this rate, and this term, what is each payment worth?

It is the mirror image of a savings projection. Instead of asking how a balance grows into the future, it asks how a balance today is spread out into a stream of equal withdrawals that exactly exhausts it — principal plus interest — over the term you choose.

How does the calculator work?

You enter four things: the principal (the premium you pay in), the annual interest rate, the term in years, and how often you want to be paid — the payout frequency (monthly, quarterly, or annually). The calculator converts the annual figures into per-period figures, because the payout happens per period rather than per year:

• the periodic rate is the annual rate divided by the number of payouts per year;
• the number of periods is the term in years multiplied by the number of payouts per year.

With those two numbers it solves the present-value-of-an-annuity relationship for the payment. It then reports the payout per period, the total you receive over the whole term, and how much of that total is interest rather than a return of your own principal.

Formula

The present value of an annuity — the lump sum that funds a stream of equal payments — is related to the payment by:

$PV = PMT \cdot \frac{1 - (1 + r)^{-n}}{r}$

Solving for the payment gives the formula the calculator uses:

$PMT = \frac{PV \cdot r}{1 - (1 + r)^{-n}}$

Where:

• $PMT$ is the payout per period.
• $PV$ is the principal (the premium paid in).
• $r$ is the interest rate per period.
• $n$ is the total number of periods.

The per-period rate and the period count come from the annual inputs:

$r = \frac{\text{annual rate}}{k}, \qquad n = k \cdot t$

where $k$ is the number of payouts per year (12 for monthly, 4 for quarterly, 1 for annually) and $t$ is the term in years.

The total payout and the interest portion follow directly:

$\text{Total payout} = PMT \cdot n, \qquad \text{Total interest} = PMT \cdot n - PV$

Zero interest rate

When the rate is zero the payment formula would divide by zero, so it collapses to simply spreading the principal evenly across the periods:

$PMT = \frac{PV}{n}$

Examples of use

1. A principal of 100,000 at a 5% annual rate, paid monthly over a 10-year term:

   • Principal $PV$ = 100000
   • Periodic rate $r = 0.05 / 12 \approx 0.00416667$
   • Periods $n = 10 \cdot 12 = 120$

   Calculation: $PMT = \frac{100000 \cdot 0.00416667}{1 - (1.00416667)^{-120}} \approx 1060.66$

   Over the full term the total payout is about $1060.66 \cdot 120 \approx 127278.62$, of which roughly 27,278.62 is interest and the remaining 100,000 is a return of your own principal.

2. The same 10-year monthly term with a 0% rate on a principal of 120,000:

   • Principal $PV$ = 120000
   • Periods $n = 120$

   Calculation: $PMT = \frac{120000}{120} = 1000$

   With no interest the annuity simply hands back your principal in equal slices: the total payout is exactly 120,000 and the interest earned is 0.

Practical notes

• The rate and the payout frequency must describe the same period. The calculator handles this for you by turning the annual rate into a per-period rate, so you only ever type the annual figure and pick the frequency.
• A more frequent payout gives a smaller amount each time but the same total over the term; the choice is about cash-flow timing, not total value.
• The interest figure is the reward for letting the insurer hold your principal: the longer the term and the higher the rate, the larger the share of the total payout that is interest rather than a return of capital.
• A zero-rate run is a useful sanity check — the total payout should equal the principal exactly, with no interest, because you are just receiving your own money back on a schedule.
• This models a fixed, immediate annuity with a level payout and a finite term. It does not price a lifetime annuity (whose length depends on life expectancy), inflation adjustments, survivor benefits, taxes, or insurer fees.

FAQs

What is the difference between an immediate and a deferred annuity?

An immediate annuity starts paying right away, within one period of the premium being paid, which is exactly what this calculator models. A deferred annuity first grows the premium for a number of years and only begins paying out later; you would project that growth phase first — for example with a future value calculator — and then annuitise the resulting balance.

Why is part of each payment not really “income”?

Each payout blends two things: interest the principal earns, and a slice of the principal itself being handed back. Only the interest is genuinely new money; the rest is a return of what you paid in. That is why the total interest earned is the total payout minus the original principal.

What happens if I choose a 0% rate?

The formula avoids dividing by zero and simply spreads the principal evenly across all the periods, so each payout is the principal divided by the number of periods and the total interest is zero.