Annuity Calculator

The Annuity Calculator Excel Template computes present and future values across five annuity structures simultaneously from a single set of inputs. Whether you're pricing a bond, valuing a pension stream, applying the Gordon Growth Model, or studying the time value of money, this spreadsheet eliminates the need to switch between calculators for each annuity type.

What You Can Calculate

This template computes 9 key outputs across all major annuity structures:

• Ordinary Annuity PV — Present value of level payments made at the end of each period. The standard formula used for loan valuations, bond pricing, and lease analysis: PMT × [(1 − (1+r)^(−n)) / r].
• Ordinary Annuity FV — Future value of level payments at period end, showing the accumulated wealth from regular contributions such as retirement savings or sinking funds.
• Annuity Due PV — Present value when payments occur at the beginning of each period (e.g., rent, insurance premiums). Always exceeds Ordinary Annuity PV by a factor of (1+r) because payments arrive one period earlier.
• Annuity Due FV — Future value of beginning-of-period payments. Equals Ordinary FV × (1+r).
• Perpetuity PV — Present value of an infinite stream of level payments: PMT / r. Used to value preferred stock, consols, and endowments.
• Growing Perpetuity PV — Present value of payments that grow at a constant rate g in perpetuity: PMT / (r − g). This is the Gordon Growth Model used extensively in equity valuation.
• Growing Annuity PV — Present value of finite payments that increase at rate g each period. Applied to salary streams, growing dividends over a finite horizon, and escalating leases.
• Total Payments (Finite Annuities) — The nominal sum of all payments (PMT × n) before accounting for the time value of money.
• Total Interest (Ordinary) — The difference between the ordinary annuity future value and total nominal payments, representing interest earned on accumulated contributions.

Required Inputs

To use this calculator, you'll need:

• Payment Amount (PMT) — The periodic payment in dollars. For growing annuities, this is the first payment amount.
• Interest Rate (r) — The per-period discount rate as a percentage. Must be on the same time basis as the number of periods (annual rate with annual periods, monthly rate with monthly periods).
• Number of Periods (n) — Total payment periods for finite annuities. Not used in perpetuity calculations.
• Growth Rate (g) — Per-period payment growth rate as a percentage. Only affects Growing Perpetuity and Growing Annuity outputs. Must be less than r for the growing perpetuity to converge.

Methodology

Each annuity type uses its standard closed-form formula. Ordinary Annuity PV = PMT × [(1 − (1+r)^(−n)) / r]; Perpetuity PV = PMT / r; Growing Perpetuity PV = PMT / (r − g); Growing Annuity PV = PMT × [1 − ((1+g)/(1+r))^n] / (r − g), with a limit formula applied when r equals g. All formulas are visible and editable in the template.

Assumptions

This model assumes:

• Ordinary annuities have payments at the end of each period; annuities due at the beginning
• All inputs (rate, growth, periods) are on the same time basis
• Constant discount rate across all periods
• Perpetuities assume an infinite payment stream; growing perpetuity requires g < r for convergence
• No taxes, fees, or compounding frequency conversions

For educational purposes only. Not financial advice.