Perpetuity Calculator
Calculate the present value of an infinite stream of payments.
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A perpetuity is a financial instrument that pays a fixed amount forever. This calculator finds its present value:
- Enter the annual payment. The amount received each year, forever.
- Enter the discount rate. Your required rate of return or the appropriate discount rate.
- Enter a growth rate (optional). If payments grow each year, enter the growth rate. This calculates a growing perpetuity. The discount rate must exceed the growth rate.
About Perpetuities
A perpetuity is a stream of equal payments that continues indefinitely. The present value formula is PV = Payment / Discount Rate. For growing perpetuities (where payments increase at a constant rate), PV = Payment / (Discount Rate - Growth Rate). Though truly infinite payments are rare, perpetuities are useful for valuing preferred stock, real estate income, and endowments.
Frequently Asked Questions
What is a perpetuity?
A perpetuity is a financial instrument that pays a fixed amount at regular intervals forever. The present value is calculated as PV = C / r, where C is the periodic payment and r is the discount rate.
Do perpetuities exist in real life?
True perpetuities are rare. The closest examples are British consols (government bonds with no maturity), some preferred stocks, and endowment funds. Many financial valuations use the perpetuity formula as an approximation for very long-lived cash flows.
What is a growing perpetuity?
A growing perpetuity has payments that increase at a constant rate each period. The formula is PV = C / (r - g), where g is the growth rate. The discount rate must exceed the growth rate, otherwise the present value is infinite.
Why must the discount rate exceed the growth rate?
If the growth rate equals or exceeds the discount rate, the present value of future payments diverges to infinity. In practical terms, this means the cash flows are growing faster than they are being discounted, making the sum unbounded.