Perpetuity Visualizations

Interactive Visualizations

Open the Perpetuity Calculator for numeric PV and growing perpetuity results.

How Perpetuity Calculations Work

Perpetuity calculations rely on the mathematical concept that as payments extend further into the future, their present value diminishes exponentially. This diminishing value allows us to calculate a finite sum for an infinite series of payments.

Perpetuity Timeline Visualization

This timeline illustrates how cash flows extend infinitely in a perpetuity, with each payment's contribution to present value diminishing over time:

Year 1
$100
9.1% of PV
Year 2
$100
8.3% of PV
Year 5
$100
6.2% of PV
Year 10
$100
3.9% of PV
Year 20
$100
1.5% of PV
∞
Infinity
$100
→ 0% of PV

Key Insight:

While payments continue forever, over 50% of a perpetuity's present value comes from the first 10-15 years of cash flows (assuming a 10% discount rate). This demonstrates why a perpetuity with infinite payments can still have a finite present value.

Perpetuity Contribution Chart

The chart below illustrates how early cash flows contribute more significantly to the present value than later ones, demonstrating why an infinite series can have a finite value:

Year 1
100.0%
Year 2
90.0%
Year 3
81.0%
Year 4
72.9%
Year 5
65.6%
Year 6
59.0%
Year 7
53.1%
Year 8
47.8%
Year 9
43.0%
Year 10
38.7%

Note how each subsequent year's contribution to present value decreases exponentially due to discounting.

Discount Rate Impact Tool

The table below shows how different discount rates affect the present value of a $100 annual perpetuity:

Discount RatePresent ValueImpact of 1% Change
2%$5,000.00±$1,666.67
4%$2,500.00±$416.67
6%$1,666.67±$185.19
8%$1,250.00±$104.17
10%$1,000.00±$66.67
12%$833.33±$45.64

Key Insight:

The relationship between discount rate and present value is non-linear. Notice how small changes in lower discount rates have a much larger impact on present value than the same changes at higher rates.

Perpetuity Comparison

Interactive Comparison: Standard vs. Growing Perpetuity

Compare how the present value changes between standard and growing perpetuities with these sample calculations:

Standard Perpetuity

Payment Amount:$100 per year
Discount Rate:8%
Growth Rate:0%
Present Value:$1,250
$100 ÷ 0.08 = $1,250

Growing Perpetuity

Payment Amount:$100 per year
Discount Rate:8%
Growth Rate:3%
Present Value:$2,000
$100 ÷ (0.08 - 0.03) = $2,000

Key Insight:

Notice that with the same payment amount and discount rate, the growing perpetuity has a significantly higher present value ($2,000 vs. $1,250). This demonstrates how even a modest growth rate can substantially increase valuation. This is why growing perpetuities are often used in terminal value calculations for businesses expected to grow steadily over time.

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