A financial annuity (or annuity) is a sequence of equal payments made at equal intervals of time. This term is used to describe financial instruments such as loan repayment or pension receipt and describes a stream of payments that have the same amount and frequency. The main parameters of an annuity include the amount of each payment (annuity member), the interval between payments (annuity period), and the total term of the annuity.
Annuity Payment
An annuity (from French annuité, Latin annuus — annual) is a financial term denoting a schedule for repaying a financial instrument (e.g., a loan or credit) in equal amounts at equal intervals (e.g., monthly or quarterly). Each annuity payment includes a portion of the principal and accrued interest.
In a broad sense, an annuity can refer to:
- A term government loan, where a portion of the debt is repaid and interest is paid annually.
- Equal monetary payments for repaying a loan or credit.
- In life insurance — a contract granting the right to regularly receive agreed sums, for example, upon retirement.
- The present value of a series of future insurance payouts.
- An accumulation scheme where identical sums are regularly deposited into an account to reach a financial goal by a certain date.
Types of Annuities by Payment Time
- Annuity in arrears (Ordinary Annuity) — payment is made at the end of each period (month, quarter). This is the most common scheme for loans.
- Annuity in advance (Annuity Due) — payment is made at the beginning of each period.
Annuity Factor
The annuity factor (K) is a value that allows determining the size of the periodic equal payment to repay a loan. The formula for its calculation (for payments in arrears) is:
K = [ i * (1 + i)^n ] / [ (1 + i)^n – 1 ]
where:
i — interest rate per period (e.g., monthly),
n — total number of periods (payments).
The amount of the periodic payment (A) is calculated as: A = K * S, where S is the initial loan amount.
Loan with Annuity Payments
Under an annuity loan repayment scheme, the borrower pays the same amount throughout the entire term. The peculiarity of this approach is that at the beginning of the loan term, a larger part of the payment goes towards interest, and a smaller part towards repaying the principal. Over time, this ratio changes in favor of the principal.
Future Value of Annuity Payments
This concept is used to calculate the amount that will be accumulated if equal payments are regularly made into an interest-bearing account. The formula for calculating the future value (FV) is as follows:
FV = X * [ (1 + r)^n – 1 ] / r
where:
X — the amount of the regular payment,
r — interest rate per period,
n — number of periods.
What is the Difference Between the Two Concepts of “Annuity”?
The text above and the article “What is an Annuity?” written earlier describe two different but interrelated concepts that are often confused. The key difference lies in the breadth of the concept and the field of application.
Annuity as a Payment Method (from this text):
- Essence: This is, first and foremost, a mathematical and financial model — a repayment schedule where payments are identical.
- Main field of application: Lending (mortgages, consumer loans). Here, an annuity is a method for calculating the monthly payment, which includes both interest and the principal.
- Key question: “How do I calculate my fixed loan payment?”
Annuity as a Financial Product (from the first article):
- Essence: This is a specific insurance or investment product that a person buys from an insurance company.
- Main field of application: Pension planning and insurance. Here, an annuity is a contract under which you receive regular income (e.g., a lifetime pension) in exchange for a lump-sum payment or a series of contributions.
- Key question: “How do I guarantee myself an income in old age?”
A Simple Analogy:
- Annuity-payment is like a form of payment (for example, a fixed monthly subscription fee for a phone). It’s a way of paying money.
- Annuity-product is like the service itself (network access, minutes, gigabytes). It’s what you get for your money.
Thus, the difference is fundamental:
In the first case, an annuity is a way to give money (for a loan). In the second case, an annuity is a way to receive money (as a pension or regular income). Both use the same mathematical model of equal payments but are applied for completely opposite financial purposes.
