Annuity Calculator

Created by Tibor Pál, PhD candidate
Reviewed by Jack Bowater and Dominik Czernia, PhD
Last updated: Jan 13, 2023

The annuity calculator is a well-featured universal tool that makes it easy to compute any of the missing element in an annuity construction, which are namely:

  • Initial deposit or the present value (PV) of the annuity;
  • Final balance or the future value (FV);
  • Annuity amount which is the periodic deposit or withdrawal (or the series of payments made at equal intervals);
  • Time length or the annuity term; and
  • Rate of return or interest rate.

What's more, you can analyze the result by following the progress of balances in the dynamic chart or the annuity table. You can apply the annuity calculator for a wide range of annuities. For example, you can use it either for regular deposits or withdrawals, for multiple frequencies, or you can compare ordinary annuity vs. annuity due.

In the following, we explain what the annuities definition is and show you some annuity examples to provide better insight into how do annuities work. You can also read about the types of annuity and learn the growing annuity formula.

If you would like to learn more about annuities, check our time value of money calculator or the annuity payout calculator.

What is the annuities definition? - How do annuities work?

Annuities are one of the most fundamental financial structures. To put it simply, any financial product that involves a series of payments made at equal intervals is an annuity. But let's take a closer look at the annuities definition. The series of payments can be either deposits (with positive signs) or withdrawal (with negative signs). Therefore, if you make regular deposits into a savings account, monthly home mortgage, monthly insurance account or pension plan, you happen to face an annuity.

However, in practice and in everyday life annuity meaning takes a more explicit form. So, what does annuity mean? Buying an annuity usually refers to investment plans, for example insurance products, that provide a steady stream of income in retirement. For example, you can buy an annuity that requires a single upfront payment, or a series of payments to the insurance company. Then, the insurance company pays you either one lump-sum or multiple payments if the insurance pays out.

Types of annuity

As you probably already know, annuities have many faces. In general, the types of annuity are classified according to the following features.

  1. Timing of payments - Ordinary annuity vs. annuity due
  • Ordinary annuity or annuity-immediate - Payments are made at the end of the periods - mortgages, car loans, and student loans are conventionally ordinary annuities.

  • Annuity due - Payments are made at the beginning of each period - rental lease payments, life insurance premiums are considered annuity due.

  1. Contingency of payments - Guaranteed annuities vs. contingent annuities
  • Annuities certain or guaranteed annuities - It provides payments that will be paid over a period fixed in advance. An example of this is the NPS scheme in India.

  • Contingent annuities - It pays over the annuitant's remaining lifetime - a typical example is a life annuity.

  1. Variability of payments
  • Fixed annuities - It guarantees a fixed return on the initial investment. The Securities and Exchange Commission does not regulate fixed annuities.

  • Variable annuities - It makes a direct annuity investment into various funds especially created for variable annuities. They are registered products that are regulated by the SEC in the United States of America.

  • Equity-indexed annuities - The annuity payouts are linked to an index. Typically, the minimum payment will be 0%, and the maximum will be predetermined. The credited amount to the customer depends on the performance of the underlying index.

  1. Deferral of payments - Immediate vs. deferred annuity
  • Deferred annuity - The payments begin only after a certain period.
  • Immediate annuity - An annuity which begins payments without a deferral period.

Note, that the present annuity calculator can deal exclusively with fixed immediate annuities.

How to use the annuity calculator? - Annuity examples

Below is a short instruction on how to use the annuity calculator:

1. Annuity specifications

  • Subject of interest:
    • Initial deposit - present value (PV);
    • Final balance - future value (FV);
    • Annuity amount - periodic deposit or withdrawal;
    • Time length - annuity term;
    • Rate of return - interest rate.
  • Direction of payment
    • Deposit;
    • Withdrawal.
  • Annuity payment frequency - The regularity of annuity payouts;
  • Type of annuity - You can choose between an annuity due (beginning of period) or an ordinary annuity (end of period).
  • Compounding frequency - The frequency interest is added to the principal balance of your investment, or, in other words, how often the earned return or interest is reinvested; and
  • First period starts from - the first day of the annuity.

2. Main specifications

  • Initial deposit - The present value of the annuity, that is, the balance at the beginning of the annuity.
  • Annuity amount - The amount of regular deposit or withdrawal.
  • Length of annuity - The interval during which the annuity pays.
  • Rate of return - The interest rate by which an annuity grows each year.
  • Annual growth rate - By this option, you can set a specific rate of change (increase or decrease) in your annuity payout.
  • periodic growth rate - The percentage growth rate of the periodic deposits of withdrawals. Note that periodic and annual growth rates are linked together: the other will be calculated according to annuity frequency if you set one.

When you set all the required parameters, you will immediately see the results summarized in a table. You can also follow the progress of your annuity balance in a dynamic chart and annuity table of the payment schedule.

The best way to demonstrate the strengths of the annuity calculator is to take some annuity examples.

  1. Annuity with fixed deposits

Let's assume you decide to put aside 100 dollars at the end of each month and pay into an annuity where the guaranteed interest rate is 5 percent, compounded monthly. What will be the future value of your annuity after ten years?

  • Initial balance = $0
  • Annuity payment = $100
  • Annuity frequency = Monthly
  • Type of annuity = Annuity due
  • Length of annuity = 10 years
  • Interest rate = 5%
  • Compounding method = Monthly

After setting the above parameters, you can read that the annuity's future value is $15,528.23.

  1. Annuity with fixed withdrawal

Let's say you have 10,000 dollars savings and you decide to buy an annuity with a 5 percent interest rate (compounded monthly) where you can withdraw 100 dollars at the beginning of each month. What will be the balance of your annuity after ten years?

  • Initial balance = $10,000
  • Annuity payment = -$100
  • Annuity frequency = Monthly
  • Type of annuity = Annuity due
  • Length of annuity = 10 years
  • Interest rate = 5%
  • Compounding method = Monthly

After setting the above parameters, you will see that the annuity's future value is $877.17.

The growing annuity formula

With the present annuity calculator you can also find out the future value of a growing annuity. In the case of growing annuity, the amount of a series of cash flows, or payments, grows at a proportionate rate. The most straightforward growing annuity formula takes the following form:

FV = P * ((1 + r)n - (1 + g)n) / (r - g)),

Where:

  • FV - Future value of the growing annuity;
  • P - The amount of the series of deposits (positive sign) or withdrawals (negative sign) made at equal intervals;
  • r - Interest rate;
  • g - Growth rate; and
  • n - Number of periods.

Disclaimer

You should consider the annuity calculator as a model for financial approximation. All payment figures, balances, and interest figures are estimates based on the data you provided in the specifications that are, despite our best effort, not exhaustive.

For this reason, we created the calculator for instructional purposes only. Still, if you experience a relevant drawback or encounter any inaccuracy, we are always pleased to receive useful feedback and advice.

Tibor Pál, PhD candidate
Annuity specifications
Subject of interest
Final balance
Direction of payment
Deposit
Annuity payment frequency
Monthly
Type of annuity
Annuity due
Compounding frequency
Monthly
First period starts from...
Main specifications
Initial deposit
$
Annuity amount
$
Length of annuity
yrs
Rate of return
%
Annual growth rate
%
Periodic growth rate
%
Results
The final balance (future value) of your annuity is $84,113.28.
Opening balance$0.00
Final balance$84,113.28
Monthly deposit$1,000.00
Total deposit$72,000.00
Total return$12,113.28
Number of deposits72
Last deposit onJan. 6, 2029
Display...
chart of balances
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