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
- Loan Repayments: Homebuyers often pay a fixed mortgage amount at the end of each month.
- Retirement Income: An individual receiving pension payments at the end of each month or year.
- Investment Annuities: Fixed investment annuities furnish payouts at the end of each defined period.
- 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.
- Annuity Due: An annuity where payments are made at the beginning of each period.
- Present Value (PV): The current value of a future sum of money or stream of cash flows given a specified rate of return.
- Future Value (FV): The value of a current asset at a specified date in the future based on an assumed rate of growth.
- Fixed Annuity: An annuity that provides regular, guaranteed payments for the duration of the contract.
- 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
Fundamentals of Annuity in Arrears: Finance Basics Quiz
### What is a primary feature of an ordinary annuity?
- [ ] Payments are made at the beginning of each period.
- [x] Payments are made at the end of each period.
- [ ] Payments vary based on inflation.
- [ ] Payments decrease over time.
> **Explanation:** The main feature of an ordinary annuity is that payments are made at the end of each consecutive period.
### Which of the following is an example of an ordinary annuity?
- [ ] Rent payments
- [ ] Insurance premiums
- [x] Mortgage payments
- [ ] Utility bills
> **Explanation:** Mortgage payments are typically made at the end of the month, making them an example of an ordinary annuity.
### How is the present value of an annuity in arrears calculated?
- [ ] Using the formula for compound interest.
- [x] Using the present value formula for an ordinary annuity.
- [ ] By multiplying payment by number of periods.
- [ ] Using the future value formula for an annuity due.
> **Explanation:** The present value of an ordinary annuity is calculated using a specific present value formula considering payments, interest rate, and number of periods.
### How do tax treatments differ for annuity payments?
- [x] Interest portions of an ordinary annuity can often be tax-deductible.
- [ ] Principal payments of an annuity are tax-deductible.
- [ ] All annuity payments are non-taxable.
- [ ] Tax treatments do not differ between ordinary and due annuities.
> **Explanation:** Interest portions on loan repayments in ordinary annuities can often be tax-deductible, such as in home mortgages.
### Which calculation is relevant for determining how much will be received from an annuity in the future?
- [ ] Present Value
- [x] Future Value
- [ ] Net Present Value
- [ ] Internal Rate of Return
> **Explanation:** The future value calculation is used to determine the amount received from an annuity in the future.
### In practical scenarios, what is an annuity due typically used for?
- [ ] Stock investments
- [ ] Utility bills
- [ ] Lump-sum lottery payments
- [x] Lease agreements
> **Explanation:** Annuity due is typically used in lease agreements where payments are made at the beginning of each period.
### What distinguishes an ordinary annuity from a compound annuity?
- [x] Payment timing within the period.
- [ ] Interest rate application.
- [ ] Principal amount.
- [ ] Additional returns involvement.
> **Explanation:** The primary distinction of an ordinary annuity is the payment timing at the end versus the beginning of each period, which is different from compound annuities.
### What term is used to describe the calculation of the current worth of a set of future periodic payments?
- [x] Present Value
- [ ] Interest Rate
- [ ] Future Value
- [ ] Compound Interest
> **Explanation:** Present Value refers to the current worth calculation of future periodic payments.
### Why are annuities important for retirement planning?
- [ ] They guarantee investment performance.
- [ ] They are always tax-free.
- [x] They provide a predictable income stream.
- [ ] They include health insurance benefits.
> **Explanation:** Annuities are important for retirement planning as they provide a predictable stream of income, which is vital for future financial stability.
### Which concept determines how much should be invested presently to achieve desired periodic returns in the future?
- [x] Present Value
- [ ] Future Value
- [ ] Amortization Schedule
- [ ] Yield Calculation
> **Explanation:** Present Value determines how much should be invested now to achieve specific future periodic returns.
Thank you for exploring the fundamentals of annuities in arrears. Dive into more quizzes to hone your financial knowledge!
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