<p>Simplest explanation is that this is because money tomorrow is worth less than money today, and 1 dollar infinitely far in future will have (almost) no value today. Most of the value of perpetuity comes from several nearest cash flows.</p>
<p>You could also visualize this without doing explicit calculations. With 10% discount rate annual payment of 100 dollars will be worth 1000 dollars. A 10 year annuity of 100 dollars will be worth over 600 dollars. Hence, most of the present value that perpetuity has is solely due to the  payments in first 10 years. A 35 year annuity will already have present value of almost 1000 dollars, so after 35 year there is almost no difference between annuity of 100 dollars and perpetuity.</p>
<p>I think a graph with a value of perpetuity plotted along values of annuities from 1y-50y, would make this easy to understand.</p>

CC BY-SA 4.0
2024-06-26T12:59:04.730Z
I completely agree with this explanation technically. However, I find your second paragraph to be too complex for most people intuitively. I am really hoping there is a simpler explanation.
escapecharacter
CC BY-SA 4.0
2024-04-07T19:49:23.510Z
2024-04-07T19:49:23.510Z
1muflon1
<p>Let’s say there exists an asset that is known to produce $1 of liquid value annually, indefinitely.</p>
<p>In practice, this asset is worth a finite amount of money. However, to a naive intuition one could argue it is worth infinite money. What’s the simplest explanation for why its worth is only finite?</p>
<p>NOTE: I am aware of time-value-of-money calculations; I actually have an applied math degree from a long time ago. I am aware that infinite sums of monotonically decreasing positive integers can have a finite value; what I’m looking for is the easiest way for a person who isn’t familiar with this mathematics to pick up this intuition.</p>
<p>This is relevant to your average person, as sometimes there’s unhelpful discourse around treating “passive income” as much higher than it genuinely is.</p>

CC BY-SA 4.0
2024-04-07T22:43:33.480Z
Presumably, someone who thinks such an asset has infinite value would buy such an asset in large amounts.
Michael Greinecker
<time-series><interest>
Simplest explanation of “Why isn’t an asset that produces recurring reliable dividends worth infinite money?”
escapecharacter
# Simplest explanation of “Why isn’t an asset that produces recurring reliable dividends worth infinite money?”

(Asked by: username_0 on 2024-04-07)

Let’s say there exists an asset that is known to produce $1 of liquid value annually, indefinitely.

In practice, this asset is worth a finite amount of money. However, to a naive intuition one could argue it is worth infinite money. What’s the simplest explanation for why its worth is only finite?

NOTE: I am aware of time-value-of-money calculations; I actually have an applied math degree from a long time ago. I am aware that infinite sums of monotonically decreasing positive integers can have a finite value; what I’m looking for is the easiest way for a person who isn’t familiar with this mathematics to pick up this intuition.

This is relevant to your average person, as sometimes there’s unhelpful discourse around treating “passive income” as much higher than it genuinely is.

**Tags:** time-series, interest
> **Comments:**
> **username_1**: Presumably, someone who thinks such an asset has infinite value would buy such an asset in large amounts.  

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## 1 answers

### Answer by username_2 on 2024-04-07. Score: 2

Simplest explanation is that this is because money tomorrow is worth less than money today, and 1 dollar infinitely far in future will have (almost) no value today. Most of the value of perpetuity comes from several nearest cash flows.

You could also visualize this without doing explicit calculations. With 10% discount rate annual payment of 100 dollars will be worth 1000 dollars. A 10 year annuity of 100 dollars will be worth over 600 dollars. Hence, most of the present value that perpetuity has is solely due to the payments in first 10 years. A 35 year annuity will already have present value of almost 1000 dollars, so after 35 year there is almost no difference between annuity of 100 dollars and perpetuity.

I think a graph with a value of perpetuity plotted along values of annuities from 1y-50y, would make this easy to understand.

> **Comments:**
> **username_0**: I completely agree with this explanation technically. However, I find your second paragraph to be too complex for most people intuitively. I am really hoping there is a simpler explanation.  

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