Annuity in Arrears

An annuity in arrears, also known as an ordinary annuity, is a series of equal payments made at the end of consecutive periods over a fixed length of time. It contrasts with an annuity due, where payments are made at the beginning of each period.
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Definition

An annuity in arrears, also referred to as an ordinary annuity, represents a series of equal cash flows made at the end of each period for a specified tenure. Common examples include recurring loan payments, such as mortgages and car loans, as well as dividend distributions.

Examples

  1. Loan Repayments: Homebuyers often pay a fixed mortgage amount at the end of each month.
  2. Retirement Income: An individual receiving pension payments at the end of each month or year.
  3. Investment Annuities: Fixed investment annuities furnish payouts at the end of each defined period.
  4. Dividends: Some companies distribute dividends to shareholders at the end of each fiscal quarter.

Frequently Asked Questions (FAQs)

Q1: How does an ordinary annuity differ from an annuity due? A1: In an ordinary annuity, payments are made at the end of each period, whereas in an annuity due, payments are made at the beginning of each period.

Q2: What are some typical usage scenarios for an annuity in arrears? A2: Common scenarios include mortgage payments, bond interest payments, and recurring business expenses.

Q3: How is the present value of an ordinary annuity calculated? A3: The present value of an ordinary annuity is calculated using the formula: \( PV = P \cdot \frac{1 - (1 + r)^{-n}}{r} \), where \( P \) is the payment amount, \( r \) is the interest rate per period, and \( n \) is the number of periods.

Q4: Are there any tax implications of receiving or paying an annuity in arrears? A4: Yes, the tax treatments can vary. For instance, interest portions of loan repayments are often tax-deductible for businesses and individuals depending on the type of loan (e.g., home mortgage).

Q5: Can an ordinary annuity become an annuity due and vice versa? A5: Yes, by adjusting the timing of payments. Contracts or agreements can often be renegotiated to reflect the desired structure.

  1. Annuity Due: An annuity where payments are made at the beginning of each period.
  2. Present Value (PV): The current value of a future sum of money or stream of cash flows given a specified rate of return.
  3. Future Value (FV): The value of a current asset at a specified date in the future based on an assumed rate of growth.
  4. Fixed Annuity: An annuity that provides regular, guaranteed payments for the duration of the contract.
  5. Variable Annuity: An annuity with payments that vary based on the performance of an investment portfolio.

Online References

Suggested Books for Further Studies

  • “Annuities For Dummies” by Kerry Pechter
  • “The Only Guide to a Winning Bond Strategy You’ll Ever Need: The Way Smart Money Invests in Bonds” by Larry Swedroe
  • “Investing in Annuities” (Financial Management Association Survey and Synthesis) by Jerry R. Green
  • “Modern Investment Theory” by Robert A. Haugen

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