Annuity in Arrears

Overview

An “Annuity in Arrears,” also known as an “Ordinary Annuity,” refers to a series of equal payments made at the end of a consistent time period. Examples include monthly mortgage payments, or dividend distributions from an investment. Because payments are made at the end of each period, the calculation of present value and future value differs from an annuity due, which pays at the beginning of each period.

Examples

Monthly Mortgage Payment: A borrower makes payments at the end of each month.
Bond Coupon Payments: Investors receive interest payments at the end of every six months.
Dividends: Investors receive quarterly dividends at the end of each quarter.

Frequently Asked Questions

Q: What is the difference between an annuity in arrears and an annuity due?

A: The main difference is the timing of payments. An annuity in arrears makes payments at the end of each period, whereas an annuity due makes payments at the beginning of each period.

Q: How do you calculate the present value of an annuity in arrears?

A: The formula for the present value \(PV\) of an ordinary annuity is:

\[ PV = PMT \times \left( \frac{{1-(1+r)^{-n}}}{r} \right) \]

where:

\(PMT\) = payment amount per period
\(r\) = interest rate per period
\(n\) = total number of payments

Q: Is an ordinary annuity more advantageous than an annuity due?

A: It depends on the investor’s needs. An ordinary annuity results in a lower present value calculation because payments are delayed, whereas payments are made sooner in an annuity due, resulting in a higher present value.

Annuity Due: A type of annuity where payments are made at the beginning of each period.
Present Value: The current worth of a sum of money to be received or paid in the future, discounted at a specific interest rate.
Future Value: The value of a sum of money at a specific point in the future, accounting for interest or investment growth over time.
Perpetuity: An annuity that continues indefinitely, paying out a fixed sum at regular intervals.

Online Resources

References

Bodie, Zvi, et al. “Investment Management.” McGraw-Hill Higher Education, 2013.
Clements, Jonathan. “Personal Finance for Dummies.” John Wiley & Sons, 2013.
Fabozzi, Frank J. “Fixed Income Analysis.” John Wiley & Sons, 2007.

Suggested Books for Further Studies

“Principles of Corporate Finance” by Richard A. Brealey, Stewart C. Myers, and Franklin Allen.
“Investments” by Zvi Bodie, Alex Kane, and Alan J. Marcus.
“Personal Finance” by Jack R. Kapoor, Les R. Dlabay, and Robert J. Hughes.
“Financial Management: Theory & Practice” by Eugene F. Brigham and Michael C. Ehrhardt.
“The Mathematics of Financial Derivatives: A Student Introduction” by Paul Wilmott, Sam Howison, and Jeff Dewynne.

Real Estate Basics: Annuity In Arrears Fundamentals Quiz

### What is the primary characteristic of an annuity in arrears (ordinary annuity)? - [ ] Payments are made immediately. - [x] Payments are made at the end of each period. - [ ] Payments vary in amount. - [ ] Payments are irregular. > **Explanation:** In an annuity in arrears (ordinary annuity), payments are consistently made at the end of each specified period. ### How does an ordinary annuity compare to an annuity due in terms of present value calculation? - [ ] An annuity in arrears has a higher present value. - [x] An annuity in arrears has a lower present value. - [ ] Both types have the same present value. - [ ] The present value cannot be calculated for annuities. > **Explanation:** An ordinary annuity has a lower present value than an annuity due because payments are made later, reducing their current worth due to the time value of money. ### What formula is used to calculate the present value of an ordinary annuity? - [ ] \\( PV = PMT \times (1+r)^n \\) - [x] \\( PV = PMT \times \left( \frac{{1-(1+r)^{-n}}}{r} \right) \\) - [ ] \\( PV = PMT \times (1-r)^n \\) - [ ] \\( PV = PMT \times \left( \frac{{1-(1-r)^{-n}}}{r} \right) \\) > **Explanation:** The formula for calculating the present value of an ordinary annuity is \\( PV = PMT \times \left( \frac{{1-(1+r)^{-n}}}{r} \right) \\). ### Which of the following is an example of an ordinary annuity? - [ ] Lease payments made at the start of each month. - [x] Mortgage payments made at the end of each month. - [ ] Royalties received at the beginning of each year. - [ ] Payments made randomly within a year. > **Explanation:** Mortgage payments made at the end of each month are an example of an ordinary annuity. ### What is another common term for an annuity in arrears? - [ ] Immediate annuity - [x] Ordinary annuity - [ ] Perpetuity - [ ] Deferred annuity > **Explanation:** An annuity in arrears is commonly referred to as an ordinary annuity. ### Among the following options, what best describes when payments of an ordinary annuity are made? - [x] At the end of each period. - [ ] At the beginning of each period. - [ ] Payment timing fluctuates. - [ ] Payments are made bi-annually only. > **Explanation:** Payments of an ordinary annuity are made at the end of each financial period. ### Why does an ordinary annuity have a lower present value compared to an annuity due? - [x] Because payments are deferred until the end of each period. - [ ] Because payments are made immediately. - [ ] Because payments are higher in amount. - [ ] Because it does not accumulate interest. > **Explanation:** An ordinary annuity has a lower present value because the payments are deferred until the end of the period, reducing their current value due to the time value of money. ### What happens to the future value of an ordinary annuity if the interest rate increases? - [ ] Decreases - [x] Increases - [ ] Remains the same - [ ] Unchanged > **Explanation:** The future value of an ordinary annuity increases if the interest rate increases because the money invested earns more interest over time. ### How frequently are bond coupon payments made in a typical ordinary annuity structure? - [ ] Monthly - [x] Semi-annually - [ ] Quarterly - [ ] Annually > **Explanation:** In a typical ordinary annuity structure, bond coupon payments are made semi-annually. ### For a given payment amount and interest rate, which has a higher future value: annuity due or ordinary annuity? - [x] Annuity due - [ ] Ordinary annuity - [ ] Both are equal - [ ] It depends on the market conditions > **Explanation:** An annuity due has a higher future value because payments are made at the beginning of each period, allowing interest to accumulate for an additional period compared to an ordinary annuity.

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