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Annuity Calculator

Calculate annuity payments, present value, and future value

Tool Overview

The Annuity Calculator helps you plan for retirement, loans, or investments by calculating regular payment amounts, present value, and future value of an annuity. An annuity is a series of equal payments made at regular intervals.

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How It Works

The Annuity Calculator uses standard time value of money formulas to calculate Present Value (PV) and Future Value (FV) for different types of annuities based on a given payment amount.

Formulas Used

Ordinary Annuity (End-of-period payments)

PV = PMT × (1 - (1 + r)^(-n)) / r FV = PMT × ((1 + r)^n - 1) / r

Annuity Due (Beginning-of-period payments)

PV = PMT × (1 - (1 + r)^(-n)) / r × (1 + r) FV = PMT × ((1 + r)^n - 1) / r × (1 + r)

Deferred Annuity

PV = Ordinary/Due PV × (1 + r)^(-k) Where: k = Number of deferral periods

Perpetuity (Infinite payments)

PV = PMT / r FV = Infinite

Variable Definitions

PMT = Payment amount per period r = Periodic interest rate n = Total number of payment periods k = Deferral periods (for deferred annuity)

Annuity Types

  • Ordinary Annuity: Payments are made at the end of each period.
  • Annuity Due: Payments are made at the beginning of each period, earning interest for an extra period.
  • Deferred Annuity: Payments start after a specified number of deferral periods.
  • Perpetuity: Payments continue indefinitely, with finite present value but infinite future value.

Key Assumptions

  • Fixed interest rate: The interest rate remains constant throughout the annuity period.
  • Equal payments: Each payment amount is the same throughout the annuity term.
  • Positive values only: Negative values are validated and rejected to ensure meaningful financial calculations.

The tool calculates both PV and FV simultaneously, highlighting the selected calculation type.

Features

  • Support for multiple annuity types: Ordinary, Due, Deferred, and Perpetuity
  • Calculate Present Value (PV) and Future Value (FV)
  • Flexible payment amount input
  • Adjustable interest rate and number of periods
  • Deferred annuity with deferral period support

Usage Examples

Example 1: Ordinary Annuity - Future Value

Annuity Type: Ordinary Annuity

Payment Amount (PMT): $1,000

Interest Rate (r): 5%

Number of Periods (n): 12

Calculate: Future Value (FV)

  • Future Value: $13,400.96
  • Present Value: $8,863.25

Example 2: Annuity Due - Present Value

Annuity Type: Annuity Due

Payment Amount (PMT): $500

Interest Rate (r): 4%

Number of Periods (n): 24

Calculate: Present Value (PV)

  • Present Value: $10,622.92
  • Future Value: $12,486.45

Example 3: Deferred Annuity

Annuity Type: Deferred Annuity

Payment Amount (PMT): $2,000

Interest Rate (r): 6%

Number of Periods (n): 10

Deferral Periods (k): 5

  • Present Value: $11,469.92
  • Future Value: $26,361.59

FAQ

What is an annuity?

An annuity is a financial product that provides a series of equal payments at regular intervals. It's commonly used for retirement income or loan repayments.

What's the difference between ordinary annuity and annuity due?

Ordinary annuity payments are made at the end of each period, while annuity due payments are made at the beginning. The calculator uses ordinary annuity by default.

How does compounding frequency affect results?

More frequent compounding generally leads to higher future values because interest is earned on interest more often.