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Estimation notes: Annuities and annuities

Estimation notes: Annuities and annuities

Generality

From the legal point of view, annuity is said to be a periodic (mostly annual) supply of money or other fungible things that a person, called debtor, undertakes to correspond to another, called creditor or beneficiary.
Two types of annuity are known and regulated by law: perpetual and life annuity.

Perpetual income

A perpetual annuity is constituted by the transfer to the debtor of a capital (simple annuity) or of a property (land annuity) in exchange for the payment of an annuity to a beneficiary for an unlimited time.
The annuity annuity is made equal to the annual interest on the value of the property sold, calculated at an rate agreed between the parties.
The debtor has the right, immediate or deferred (up to a maximum of 10 years in the simple annuity and 30 years in the land annuity) to free himself from the obligation to provide the service, paying a redemption price equal to the capitalization value of the annuity to the legal interest rate.
The value of an immediately redeemable annuity is equal to its redemption price (Vr = Pr = a / i). If the annuity is redeemable only after a certain number of years, its value is given by the accumulation at the moment of the estimate, at the financial rate, of the years that remain to be paid plus the discounted amount of the redemption price.

Life annuity

A life annuity is constituted by the transfer to the debtor of an asset, in exchange for the payment of an annuity to a beneficiary for his entire life or for that of another designated person. An interest rate has been agreed between the parties and the number of years of probable life of the reference person has been found on the mortality tables, the annuity annuity is to be calculated as the depreciation or reintegration fee (depending respectively on the transfer of ownership of the asset the establishment of the annuity or its extinction) of the value of the property sold for this number of years.
A life annuity cannot be redeemed, and its value is at all times equal to the initial accumulation of the financial rate of the annuities that remain to be paid, according to the probability of life of the beneficiary or the designated person.

The right of the beneficiary of a perpetual or life annuity is guaranteed by a mortgage on a debtor's real estate. the value of the asset so burdened is at all times equal to the difference between the market value it would have if it were free and the value of the annuity.


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