---
title: the annuity that ends the perpetuity
canonical_url: https://ensurance.app/guide/the-annuity-that-ends-the-perpetuity
markdown_url: https://ensurance.app/guide/the-annuity-that-ends-the-perpetuity.md
subtitle: "price the owner's forever, pay it over a dated path or at once, and the payments have an end date"
category: nature-finance
---

# the annuity that ends the perpetuity

*price the owner's forever, pay it over a dated path or at once, and the payments have an end date*

A **perpetuity** pays the same amount every year with no end date. Its value today is the payment divided by the rate: $20,000 a year at 4% is worth $500,000. An **annuity** pays for a set number of years and then stops. Its value today is the payment times an annuity factor for that rate and term.

Land is priced like a perpetuity. A buyer pays roughly the rent the land can earn, divided by a rate, because the deed carries that rent forever. Whoever can pay the most capitalized rent decides what the land becomes. Below, one invented parcel: price the owner's perpetuity and pay it over a dated path or at once. When the payments are done and the legal documents release the land, no owner holds a private claim on its future rent.

The meadow, the creek and the soil hold water and grow grass whether anyone collects rent on them or not. *Ensurance* is how a parcel can be paid off the owner's rent roll and held for itself. It is not the land, and it is not a better landlord. A parcel funded year by year is *ensured*; one paid out and legally locked is at *entrust*.

:::johnson
**an annuity with an end date, in place of a rent with none.**

Both are worth the same today. Only one of them ends.
:::

*Illustrative arithmetic. Not a quote for any parcel, and not legal, tax or investment advice.*

## perpetuity vs annuity, on one parcel

Picture a 160-acre hay meadow along a creek, farmed by a tenant on a cash-rent lease. After property tax and upkeep, the owner clears **$20,000 a year**. That rent is ordinary, legitimate income; [what cash rent is already pricing](/guide/what-cash-rent-is-already-pricing?from=guide) shows the tenant is mostly paying for the topsoil and the water.

Use one rate for everything, **4% a year**, with payments at each year-end.

| measure | formula | result |
|---|---|---:|
| The owner's perpetuity | $20,000 ÷ 4% | $500,000 |
| Annuity factor, 25 years | AF(4%, 25) = (1 − 1.04^−25) ÷ 0.04 | 15.6221 |
| 25 years of rent, valued today | $20,000 × 15.6221 | $312,442 |
| Everything after year 25, valued today | $500,000 − $312,442 | $187,558 |

The last row is the **residual**: the rent from year 26 onward, forever, in today's money. Check it another way: $500,000 discounted 25 years at 4% is $500,000 ÷ 1.04^25 = $187,558. Same number. (Checks use unrounded values.)

Real land prices often run above rent ÷ rate, because buyers also price rent growth and the chance of a higher use. A real quote states its price basis and adds restoration and fees.

## the gap is what the owner sells

A lease, even a long one, never touches the residual. The tenant gets years of use; the owner keeps the forever part, which is what makes the meadow saleable to the next bidder. Better lease terms leave the $187,558 where it was.

Ending the perpetuity means the owner gives up the residual, and is paid for it. Spread the $500,000 over a dated 25-year path at the same 4%:

| | what the owner receives | for how long | value today at 4% |
|---|---:|---|---:|
| **Keep the lease** | $20,000 a year | forever | $500,000 |
| **25-year path** | $500,000 ÷ 15.6221 = $32,006 a year | 25 years, then nothing | $500,000 |

Same value, different shape, on one condition: the $32,006 replaces the rent. The owner stops collecting the $20,000; the tenant's rent goes to the path instead. The other **$12,006 a year** pays for the residual, and over 25 years at 4% it is worth the same $187,558. The owner receives the perpetuity's present value and no more, in a form that ends.

The two are equal only at one rate. A real owner swaps land whose rent tends to rise for a level payment from a payer who could default, and a sale is taxed differently from rent; a real path prices those. The total, $800,150 over 25 years, looks larger than $500,000 only because it is spread out. Totals are not the comparison; present values are, which is the point of [the quote beside the cost of doing nothing](/guide/the-quote-beside-the-cost-of-doing-nothing?from=guide).

## three paths on the same parcel

Three funding paths are designed. A real quote prices each at its own rate; here everything sits at 4% so the shapes compare. None of these figures is a quote or a rate for any ensurance instrument.

| path | what is paid | illustrative, at 4% | where it ends |
|---|---|---:|---|
| **Ensured, year by year** | a yearly premium for protection while it is funded | $20,000 a year | never; the claim on the land stays |
| **Dated entrust, 15 years** | $500,000 ÷ AF(4%, 15) = $500,000 ÷ 11.1184 | $44,971 a year, $674,565 in all | entrust, under the legal documents |
| **Dated entrust, 25 years** | $500,000 ÷ 15.6221 | $32,006 a year, $800,150 in all | entrust, under the legal documents |
| **Entrust now** | one payment | $500,000 | entrust, under the legal documents |

Look at the first row. Ensured at the same rate costs exactly the rent, every year, forever: a perpetuity again, paid to keep the land as it is. That can be the right start. It is not an exit. The other three carry the same $500,000 today; they differ in timing.

## who holds the land during the path

A dated path is a payment stream, and the land is not free of claims on day one. Whoever carries the cost until it is repaid may keep title or hold the land as security. Two common shapes:

- **The owner carries it.** They keep title as security and receive the annuity directly, much as a seller under an installment land contract keeps the deed until the last payment.
- **Capital carries it.** Someone pays the owner up front and holds title or security while premiums repay that cost.

Either way, if the payments stop, the party carrying the cost keeps the property, as the [natural assets manual](/manual/natural-assets?from=guide) says. Completing the payments does not release title by itself; the release is written in the documents, and [buy the land-use decision](/guide/buy-the-land-use-decision?from=guide) covers which rights a deal has to reach.

## the tenant stays

Nothing in the path requires the farmer to leave.

Routing the tenant's rent to the path is a design idea, not a described feature. The meadow's $20,000 would cover most of each $32,006 payment; the remaining $12,006 a year would come from the people who depend on what the meadow does (the town downstream, the irrigators below it) and from certificate sales. Each deal writes this into its agreements.

## at entrust, the lease becomes a use agreement

When the path completes and the legal work is done, the land is held for itself: by a foundation, a local land trust, a group of stewards, or, through a holder or legal wrapper with the place as beneficiary, by the land itself. [Permanent protection has to survive us](/guide/permanent-protection-has-to-survive-us?from=guide) sets out what that legal state has to include.

The design is that the lease is re-papered as a term use agreement: **same farmer, same field, a different payee.** The fee goes to the place's account, where care comes first, instead of to an owner. It is not necessarily lower than today's rent. It is contract rent for use, and legitimate. What is gone, by design, is the perpetuity: nobody can sell the meadow, borrow against it or capitalize its rent into a price. Use is granted for a term by application, need or merit under the place's governance. A certificate or coin is not a use right unless one is built into the instrument, and today none is ([one token can't be your home, your vote and your visit](/guide/one-token-cant-be-your-home-your-vote-and-your-visit?from=guide)).

## what this does not claim

No parcel is at entrust yet. Entrust is the designed end state, and legal permanence at scale is still to be proven. Property tax and the cost of care remain after entrust. The land still yields; its flows serve the place and the people who depend on it. The perpetuity on the land ends. Its yield does not.

## bring a property, or talk it through

To see this on your own land, start with [how to bring a property into ensurance](/guide/how-to-bring-a-property-into-ensurance?from=guide), then the two legal reads linked above. Or [talk to someone who can run the path with you →](/contact?from=guide&topic=rent-is-a-perpetuity)

## frequently asked questions

### perpetuity vs annuity: what is the difference?

A perpetuity pays forever; its value today is payment ÷ rate. An annuity pays for a set term; its value is payment × AF(rate, term). For the same payment, the difference is the residual: everything the perpetuity pays after the annuity stops, discounted to today.

### does the tenant have to leave?

Not because of the path; an existing lease runs on. At entrust the design is a term use agreement with the place, on a term and renewal its governance sets, the fee going to the place's account.

### is the land free of debt from the first payment?

No. During a dated path the party carrying the cost may hold title or security, and keeps the property if payments fail. The aim is land free of the owner's perpetuity, of debt and of private claims at entrust, not before. Contract rent for use can continue.

## sources

[OpenStax, *Principles of Finance*, §8.1 "Perpetuities"](https://openstax.org/books/principles-finance/pages/8-1-perpetuities) — "What Is a Perpetuity?" (a series of payments that continues forever) and equation 8.1, the constant perpetuity, PV = C ÷ R

[OpenStax, *Principles of Finance*, §8.2 "Annuities"](https://openstax.org/books/principles-finance/pages/8-2-annuities) — "Calculating the Present Value of an Annuity", ordinary annuity defined, and equation 8.14, PVa = PYMT × (1 − 1 ÷ (1 + r)^n) ÷ r

[ensurance manual, natural assets](/manual/natural-assets?from=guide) — "three holds on one natural asset": fee title stays with the cost-side holder until premiums repay the cost; if premiums do not arrive, the holder still has the property; automatic onchain release of title is not live

## the series

1. [rent is a perpetuity](/guide/rent-is-a-perpetuity?from=guide) — **Read first:** why land is priced like an income that never ends, and how a parcel leaves that contest
2. [three things called rent](/guide/three-things-called-rent?from=guide) — Contract rent, economic rent and rent-seeking, and which one entrust ends
3. [a better lease is still a lease](/guide/a-better-lease-is-still-a-lease?from=guide) — What reformed leases fix, and what community land trusts and purpose trusts already do
4. [the annuity that ends the perpetuity](/guide/the-annuity-that-ends-the-perpetuity?from=guide) — Time value of money as a way out that takes nothing from anyone
5. [usufruct: the use is given, the land is held](/guide/usufruct-land-access-without-debt?from=guide) — An old idea rebuilt: use and fruits, the substance kept, the land never for sale
6. [held for itself, used by many](/guide/held-for-itself-used-by-many?from=guide) — Who holds entrusted land, who uses it, and who keeps the holder honest