Perpetuity Calculator — Level, Due, Growing

How to use this perpetuity calculator

1. Select the Perpetuity type: Level (ordinary), Perpetuity Due, or Growing.
2. Choose what to solve for (PV, C, r, or g) and fill in the other fields.
3. Click Calculate or press Ctrl/Cmd+Enter. Use Copy results to capture the summary.

Formulas

Level (ordinary): PV = C / r

Perpetuity due: PV = C + C / r (first payment today)

Growing (ordinary): PV = C / (r − g) (valid only if r > g)

Growing due (first payment today, growth from next period): PV = C × (1 + r) / (r − g)

Perpetuities — Definitions, Assumptions, and Practical Tips

This calculator values perpetuities—assets that pay a fixed cash flow each period, indefinitely. Enter a per-period cash flow C, discount rate r, optional growth rate g, and choose what to solve for: present value (PV), C, r, or g. Results are computed fully client-side for privacy and speed.

Choose the perpetuity type that matches your situation: Level (ordinary) assumes the first cash flow arrives next period with no growth, using PV = C / r. Perpetuity due assumes the first cash flow is received today, so the value is one extra payment higher: PV = C + C / r. For a growing perpetuity, cash flows rise at a constant rate g and the formula becomes PV = C / (r − g). If you select growing due (first payment today with growth thereafter), the standard expression is PV = C × (1 + r) / (r − g).

Rates in this tool are entered as percentages per period (e.g., type “5” for 5%). Keep units consistent: if cash flows are annual, use an annual discount rate and (if applicable) an annual growth rate. If you model quarterly or monthly cash flows, convert your rates to the same period before using the calculator.

Important guardrails are built in. A growing perpetuity only makes financial sense when r > g; if the discount rate is less than or equal to the growth rate, the formula is undefined (PV would explode). The tool also prevents division by zero and alerts you when inputs imply impossible cases, such as a perpetuity-due scenario where PV ≤ C.

Interpretation tips: PV reflects the price you would pay today, given the stated cash flow and rate assumptions. Solving for C tells you the sustainable distribution a fund or endowment could pay forever at a target rate. Solving for r gives the implied return based on a market price and promised cash flow. Solving for g reveals the growth the market is pricing in, conditional on your discount rate.

Quick example: with C = £1,000 and r = 5%, a level perpetuity has PV = £1,000 / 0.05 = £20,000. If cash flows are expected to grow at g = 2%, the growing PV is £1,000 / (0.05 − 0.02) = £33,333.33. If the first payment is today (due), the growing PV becomes £1,000 × 1.05 / 0.03 ≈ £35,000.

Educational use only — not financial advice. Always align cash-flow timing and rate conventions with your organisation’s policy.

• “Ordinary” = first cash flow next period; “Due” = first cash flow today.
• All rates are % per period; keep PV, C, r, g on the same period basis.
• Growing perpetuity requires r > g for a finite PV.
• Friendly messages appear for invalid or inconsistent inputs.