## What Is Annuity in Arrears?

Annuity in arrears refers to the payment of an equal amount of money that is made at the end of a regular term. It does not refer to an annuity product, per se, but instead refers to a payment structure that an annuity might employ. A common example of an annuity in arrears is a mortgage payment.

Annuity in arrears—a legal, accounting and actuarial term—is also known as an "ordinary annuity." The opposite of an annuity in arrears is known as an "annuity in advance" or "annuity due."

### Key Takeaways

- An annuity in arrears is the payment of money made at the end of a regular term.
- This payment could be interest or mortgage, or another recurring payment.
- The present value of annuity-in-arrears payments is lower than annuity in advance or annuity due payments.

## How Annuity in Arrears Works

Another way of describing annuity in arrears is a series of periodic, recurring payments that are due at the end of a predetermined period. Such a payment could be interest, a mortgage payment consisting of principal and interest, or any other recurring payment—most often a payment on an installment loan—that allows interest to accrue.

Other examples of this concept are the semiannual interest payments made on a bond or quarterly or annual dividend payments. While the term "in arrears" is part of "annuity in arrears," their meanings are vastly different. "In arrears" is simply used to denote that a payment is late.

## Annuity in Arrears and Present Value

Since payments on an annuity in arrears (or ordinary annuity) are made at the end of a given period, the present value of such payments is lower than in an annuity in advance or annuity due, which features a payment at the beginning of a term. The value of an annuity in arrears will decrease when interest rates rise and increase when interest rates fall.

The reason for this is that the present value of future cash payments depends on the interest rate used in calculating the present value. When the time value of money (TVM) changes, the annuity valuation changes as well.

As such, if you are the one making the payment, an annuity in arrears is preferable because of inflation and the opportunity to earn interest on investments or interest-bearing accounts given that a sum of money today is worth more than the same sum in the future. Reflexively, if you are the party receiving a payment, an annuity due (or annuity in advance) is preferable for the same reason.

## Annuity in Arrears Characteristics

There are three elements of an annuity in arrears (or ordinary annuity):

- Each payment is in the same amount (for example, a series of $100 payments).
- Each and every payment is made at the same time interval (such as monthly or quarterly for a period of a year or more).
- Each and every payment is made at the end of the specified time period (for example, a payment made on the final day of each month).