An annuity in advance, also known as an annuity-due, refers to a series of equal payments that are made at the beginning of each period. This type of annuity is commonly found in leasing agreements, where rent is typically paid at the start of each rental period.
Key Characteristics
- Payment Timing: Payments are made at the beginning of each period.
- Equal Payments: The amount of each payment is usually equal.
- Applications: Common in lease agreements, insurance premiums, and certain types of loans.
Example Scenario
Consider a landlord who leases property for five years. The rent is paid at the beginning of each year. Here, the rented payments constitute an annuity in advance.
Mathematical Representation
The present value (\(PV\)) of an annuity in advance is calculated using the following formula, where \(C\) is the payment amount, \(r\) is the interest rate per period, and \(n\) is the number of periods:
This formula differs from the present value of an ordinary annuity because payments are made at the beginning of each period, so an additional adjustment of \((1+r)\) is necessary.
Comparison with Ordinary Annuity
An ordinary annuity involves payments made at the end of each period. The two can be contrasted as follows:
| Feature | Annuity in Advance (Annuity-Due) | Ordinary Annuity |
|---|---|---|
| Payment Timing | Beginning of period | End of period |
| Present Value | Higher (due to early payment) | Lower |
Historical Context
The concept of annuities dates back to ancient times as a means of ensuring regular income for retirees. The differentiation between an ordinary annuity and annuity in advance became more pronounced as financial instruments evolved, offering more flexibility to meet various needs.
Related Terms
- Ordinary Annuity: Payments are made at the end of each period.
- Present Value (PV): The current worth of a series of future payments.
- Future Value (FV): The value of a series of payments at a specified future date.
FAQs
What is the primary difference between an annuity in advance and an ordinary annuity?
Why is the present value of an annuity in advance higher?
References
- Bodie, Z. A., Kane, A., & Marcus, A. J. (2014). Investments. McGraw-Hill Education.
- Fabozzi, F. J. (2009). Bond Markets, Analysis, and Strategies. Pearson Education.
Summary
An annuity in advance provides a structured series of payments made at the beginning of each period, often used in lease agreements and certain types of loans. Understanding the differences between an annuity in advance and an ordinary annuity, as well as how to calculate their present value, can be crucial in various financial planning and analysis scenarios.
