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Calculator Answers

Annuity Calculator

Blake Boege
Written by Blake Boege · Founder, Calculator Answers

An annuity calculator is a financial mathematics utility designed to compute the present value and future value of a series of equal periodic payments made over a specified duration. An ordinary annuity assumes payments are made at the end of each compounding period (such as monthly or annually). The future value calculation demonstrates the wealth accumulated over time through compound interest, while the present value calculation determines the lump sum equivalent needed today to fund that stream of future payments. Retirees and investors use this calculator to plan structured payouts and evaluate investment contracts.

Estimate the present value and future value of an ordinary annuity. Choose payment amount, APR, duration, and periodic payment frequency.

See also: Whole Life Insurance Calculator, Present Value Calculator, and Future Value Calculator.

Quick Answer

Calculate the future value and present value of an ordinary annuity. Enter the recurring payment amount, interest rate, number of years, and payment frequency.

Annuity specifications

$

The cash flow amount deposited or received each period.

Frequency

%

Expected annual return.

years

Total duration in years.

Annuity Mathematics

  • Ordinary Annuity: Payments are made at the end of each period. This is standard for retirement payouts, auto loans, and mortgages.
  • Future Value (FV): Represents the sum of all payments compounded over time. It shows the wealth you accumulate.
  • Present Value (PV): Represents the current value of all future payments discounted at the target APR. It shows what a future payout stream is worth to you today.
Annuity summary

Accumulated Future Value

$46,204.09

Present Value equivalent: $13,958.08

Periodic Payment$100.00 / period
Payment FrequencyMonthly
Annuity Duration20 years
Interest Rate (APR)6%
Total Contributions$24,000.00
Future Value (FV)$46,204.09
Present Value (PV)$13,958.08
Total Compound Interest Earned$22,204.09

Annuity calculations are based on ordinary annuity cash flows. Taxes, management fees, inflation, and structured contract options are not included in these math estimates.

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Examples

$100/mo at 6% APR for 20 years

FV ≈ $46,204.09 · PV ≈ $13,958.08

$500/mo at 8% APR for 10 years

FV ≈ $91,473.02 · PV ≈ $41,208.57

$1,000/yr at 5% APR for 30 years

FV ≈ $66,438.85 · PV ≈ $15,372.45

How it works

An ordinary annuity consists of a series of equal payments made at the end of each period. Future value compounding projects the growth of these payments forward, while present value discounting translates future cash flows back to today's dollar equivalent.

Future Value (FV) · FV = PMT × (((1 + i)^N − 1) / i)

Present Value (PV) · PV = PMT × ((1 − (1 + i)^−N) / i)

Where PMT is the recurring payment amount, i is the interest rate per period (APR / payments per year), and N is the total number of periods (years × payments per year).

No contribution limit applies to this calculation

This page computes the time value of a level payment stream from the payment, rate and term you enter. It is ordinary annuity arithmetic and no statutory contribution limit enters it, so none is stated here.

A limit would apply if the payments were going into a retirement plan, which is a different question from the one this tool answers. The 401k and IRA calculators carry those figures with their year and authority.

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Frequently asked questions

An annuity is a financial product that represents a series of equal payments made at regular intervals (such as monthly, quarterly, or annually). It is commonly used in retirement planning, mortgages, structured settlements, and insurance contracts.

An ordinary annuity assumes payments are made at the end of each period (the default setting modeled by this calculator). An annuity due assumes payments are made at the beginning of each period.

For a monthly rate i and total payments N, the formulas are: Future Value FV = PMT × (((1 + i)^N − 1) / i) and Present Value PV = PMT × ((1 − (1 + i)^−N) / i). If the interest rate is 0%, then FV = PV = PMT × N.

The present value (PV) is the lump sum of money you would need to invest today, at a given interest rate, to fund a specific stream of equal payments in the future. It tells you 'what a future stream of income is worth in today's dollars'.

The future value (FV) represents the total accumulated balance of all periodic payments plus compound interest at a future date. It shows 'how much your recurring contributions will grow to' over a set term.