Perpetual annuity is not something you come across every day. What is perpetual annuity? It's a business agreement where someone agrees to collect a fixed rate on an investment they've made for an indefinite period of time. Other forms of annuity often terminate after the beneficiary dies, or after the contracted period has expired. As you can imagine, there are few by-definition perpetual annuities.



Naturally, perpetual agreements require that the investment lasts forever and that the source of investment will find it wise to make payments out to the beneficiary for the rest of time. There are a few cases where a perpetual annuity formula is applied to calculate the annual payout of an annuity, but these have some stipulations as to how long the contract will last. However, there's one interesting type of actually perpetual annuity that is worth talking about.



In the 18th century, the British government created a type of bond called the Consolidated Annuities Bond. This became shortened over time to the word "consol." Consols were sold to the public without a date for future government redemption. Originally, these bonds were created with sort of the opposite thought in mind: the government could redeem them at any time. However, the annual payments (also known as the coupon) of the bond was so small that it would be more inconvenient to redeem the bonds rather than to offer the small annual payouts. The consol became, then, a de facto perpetual annuity simply because there was no reason to redeem it.

Other annuities may use perpetuity formulas without being "true" perpetual annuities. This is a common practice in Real Estate. The rate of payment assumes that the property will continue to generate the same amount of money over time for an indefinite period of time. Owners of real estate assess rates on property on tenants as rent. Assuming the value of the property itself only fluctuates with inflation, the amount collected by the landlord continues in perpetuity. If a new renter moves in, the rate remains unchanged. If they decide to sell the property to someone else, then the new owner can use the same rent structure. Or, at least, that's what I seem to be getting out of this. I could be quite wrong, but this would make sense given that perpetual annuities are payments only pay out in coupon and cannot be generally redeemed.