Ordinary Annuity

An Ordinary Annuity, also known simply as an annuity, involves a series of equal payments or receipts occurring at the end of each period over a set duration. It’s commonly used in contexts such as mortgage or loan repayments, retirement accounts, and investment portfolios.

Examples

Mortgage Payments: When someone takes out a mortgage, they typically make monthly payments. These payments form an ordinary annuity.
Retirement Accounts: Payments made into a retirement account, like an Individual Retirement Account (IRA), often occur at the end of each month or year, forming an ordinary annuity.
Bond Coupon Payments: Bonds that pay interest semi-annually at the end of each period represent an ordinary annuity for the bondholder.

Frequently Asked Questions

Q1: How is an ordinary annuity different from an annuity due?

A: In an ordinary annuity, payments occur at the end of each period, whereas in an annuity due, payments occur at the beginning of each period.

Q2: What formula is typically used to calculate the present value of an ordinary annuity?

A: The present value of an ordinary annuity can be calculated using the formula: PV = Pmt × [(1 - (1 + r)^-n ) / r]
- PV = Present Value
- Pmt = Payment amount per period
- r = Periodic interest rate
- n = Total number of payments

Q3: Can ordinary annuities be used for retirement planning?

A: Yes, ordinary annuities are commonly used in retirement planning for making or receiving regular payments towards retirement savings.

Q4: What is the future value of an ordinary annuity?

A: The future value can be calculated using the formula: FV = Pmt × [((1 + r)^n - 1) / r]
- FV = Future Value
- Pmt = Payment amount per period
- r = Periodic interest rate
- n = Total number of payments

Q5: Are loan repayments examples of ordinary annuities?

A: Yes, many loan repayments, including mortgages, car loans, and personal loans, are structured as ordinary annuities with payments due at the end of each period.

Annuity Due: An annuity where payments occur at the beginning of each period.
Present Value: The current value of a series of future payments, discounted at a specified interest rate.
Future Value: The value of a series of payments at a specific future date, including interest.
Periodic Interest Rate: The interest rate applied to each period in the annuity.

Online Resources

References

Brealey, R., Myers, S., & Allen, F. (2019). Principles of Corporate Finance. McGraw-Hill Education.
Bodie, Z., Kane, A., & Marcus, A. J. (2014). Investments. McGraw-Hill Education.
Reilly, F. K., & Brown, K. C. (2011). Investment Analysis and Portfolio Management. Cengage Learning.

Suggested Books for Further Studies

The Complete Guide to Annuities: How to Safeguard Your Future by Matthew G. Young
Principles of Investments by Bodie et al.
Valuation: Measuring and Managing the Value of Companies by McKinsey & Company Inc.

Real Estate Basics: Ordinary Annuity Fundamentals Quiz

### What payment structure is an example of an ordinary annuity? - [ ] Payments made at the start of each period - [x] Payments made at the end of each period - [ ] Random payments throughout the periods - [ ] Single lump sum payment > **Explanation:** An ordinary annuity involves regular payments made at the end of each period. ### An ordinary annuity is often used in which of the following contexts? - [x] Mortgage payments - [ ] Insurance premiums paid at the start of the month - [ ] Irregular stock dividends - [ ] Property taxes paid at the beginning of the year > **Explanation:** Mortgage payments are a classic example of an ordinary annuity where payments are made at the end of each period. ### What is the critical difference between ordinary annuities and annuity due? - [x] Timing of payments within the period - [ ] Frequency of payments - [ ] Amount of each payment - [ ] Total number of payments > **Explanation:** The critical difference is in the timing of the payments: ordinary annuities pay at the end of each period, whereas annuity dues pay at the beginning. ### How do you find the present value of an ordinary annuity’s payments? - [ ] Using the future value formula - [x] Using the present value formula for annuities - [ ] Using the loan amortization schedule - [ ] By summing all future payments > **Explanation:** Present value is calculated using the present value formula for ordinary annuities, which discounts the future payments to their present worth. ### Which kind of interest rate applies to the periods in an ordinary annuity? - [x] Periodic interest rate - [ ] Annual nominal interest rate - [ ] Fixed rate - [ ] Discount rate > **Explanation:** The periodic interest rate is applied to each payment period in an ordinary annuity. ### What must be true for a series of payments to qualify as an ordinary annuity? - [x] Equal payments made at the end of each period - [ ] Payments can be of varying amounts - [ ] Payments made at random intervals - [ ] Payments made once at the end of all periods > **Explanation:** An ordinary annuity involves equal payments made consistently at the end of each period. ### In which scenario would you not use an ordinary annuity formula? - [x] For payments made at the beginning of each period - [ ] For evenly timed mortgage payments - [ ] For end-of-period annuities - [ ] For bond coupon payments that accrue every six months > **Explanation:** If payments are made at the beginning of each period, it constitutes an annuity due, not an ordinary annuity. ### What's the key characteristic of the future value of an ordinary annuity? - [x] It includes accumulated interest - [ ] It excludes interest - [ ] It considers only the principal payments - [ ] It fluctuates randomly > **Explanation:** The future value of an ordinary annuity includes the accumulated interest over the periods. ### For which type of payment sequence is an ordinary annuity least appropriate? - [ ] Retirement withdrawals made monthly at month-end - [ ] Loan repayments made quarterly - [ ] Semi-annual bond coupon payments - [x] Utility bills paid at the beginning of each period > **Explanation:** Utility bills paid at the beginning of each period would be classified under annuity due, not ordinary annuity. ### How does the timing of payments affect the value calculations between ordinary annuity and annuity due? - [x] Ordinary annuity payments at the end of the period reduce the accumulated interest over time - [ ] There is no difference in value calculations - [ ] An annuity due generally has a lower value due to faster payments - [ ] The timing has no effect on the overall amount of interest > **Explanation:** Payments made at the end of each period accumulates less interest over time compared to those made at the beginning, affecting the value calculations between ordinary annuity and annuity due.

Ordinary Annuity