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Present Value of an Ordinary Annuity Calculator

Calculates the current value of a series of equal payments made or received at the end of each period for a specified number of periods.

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Present Value of Annuity

Formula first

Overview

This formula is a fundamental concept in finance, allowing for the valuation of future cash flows in today's terms. It discounts each future payment back to its present value and sums them up, reflecting the time value of money where a dollar today is worth more than a dollar in the future due to its earning potential. It's crucial for understanding the true worth of a stream of regular payments.

Symbols

Variables

PVA = Present Value of Annuity, PMT = Payment per Period, r = Interest Rate per Period, n = Number of Periods

Present Value of Annuity
Payment per Period
Interest Rate per Period
Number of Periods

Apply it well

When To Use

When to use: This equation is used to: 1. Value a stream of regular income, such as pension payments or lottery winnings paid out over time. 2. Calculate the present cost of a loan or mortgage, where payments are made periodically. 3. Determine the amount needed today to fund a future series of equal withdrawals, like retirement planning. 4. Evaluate investment opportunities that promise a series of fixed, periodic returns.

Why it matters: The Present Value of an Ordinary Annuity is a cornerstone of financial mathematics, underpinning critical decisions in investment appraisal, retirement planning, and loan amortization. It helps in comparing different financial products or investment strategies that involve periodic payments, ensuring that decisions are based on the true economic value. Understanding this concept is vital for personal financial planning, corporate finance, and investment analysis, as it quantifies the impact of interest rates and time on money.

Avoid these traps

Common Mistakes

  • Confusing Ordinary Annuity with Annuity Due: Incorrectly applying the ordinary annuity formula when payments are made at the beginning of the period, leading to an underestimation of the present value.
  • Inconsistent Time Units: Using an annual interest rate with monthly payments or vice-versa without proper conversion, resulting in significant calculation errors.
  • Misinterpreting 'n': Confusing the number of years with the total number of payment periods, especially when payments are more frequent than annual.

One free problem

Practice Problem

You are offered an investment that pays $500 at the end of each year for the next 10 years. If the discount rate is 6% per year, what is the present value of this annuity?

Payment per Period500
Interest Rate per Period0.06
Number of Periods10

Solve for:

Hint: Use the direct formula for Present Value of an Ordinary Annuity with the given payment, rate, and number of periods.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Brealey, Richard A., Stewart C. Myers, and Franklin Allen. Principles of Corporate Finance. McGraw-Hill Education.
  2. Ross, Stephen A., Randolph W. Westerfield, and Bradford D. Jordan. Corporate Finance. McGraw-Hill Education.
  3. Brealey, R. A., Myers, S. C., & Allen, F. (2020). Principles of Corporate Finance (13th ed.). McGraw-Hill Education.
  4. Brigham, E. F., & Houston, J. F. (2020). Fundamentals of Financial Management (16th ed.). Cengage Learning.
  5. Commonly found in introductory finance and financial mathematics textbooks.