FinanceTime Value of MoneyA-Level
NESAAQAIBAbiturAPBaccalauréat GénéralBachilleratoCambridge

Annuity Present Value Calculator

PV of a series of equal payments.

Use the free calculatorCheck the variablesOpen the advanced solver
Open Advanced Calculator
This is the free calculator preview. Advanced walkthroughs stay in the app.
Result
Ready
Present Value

Formula first

Overview

The Annuity Present Value formula calculates the current lump-sum value of a series of future equal payments made at regular intervals. It applies the concept of discounting to account for the time value of money, assuming a constant interest rate and fixed payment amounts.

Symbols

Variables

PV = Present Value, P = Payment/Period, r = Rate per Period, n = Num Periods

PV
Present Value
$
Payment/Period
$
Rate per Period
Variable
Num Periods
Variable

Apply it well

When To Use

When to use: This equation is used when evaluating 'ordinary annuities' where equal payments occur at the end of each period. It is essential for determining the initial value of loans, mortgages, or fixed income streams where the interest rate and payment periods are consistent.

Why it matters: Understanding present value allows individuals and firms to compare immediate cash totals against future payment streams. It is a fundamental tool for retirement planning, bond valuation, and calculating the true cost of borrowing.

Avoid these traps

Common Mistakes

  • Using annual rate for monthly payments.
  • Confusing annuity due.

One free problem

Practice Problem

A retiree is offered a pension that pays 5,000 dollars at the end of every year for the next 20 years. If the annual discount rate is 4 percent, what is the present value of this pension?

Payment/Period5000 $
Rate per Period0.04
Num Periods20

Solve for: PV

Hint: Use the annual interest rate as a decimal (0.04) and ensure n represents the total number of years.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Corporate Finance by Stephen A. Ross, Randolph W. Westerfield, Jeffrey F. Jaffe
  2. Principles of Corporate Finance by Richard A. Brealey, Stewart C. Myers, Franklin Allen
  3. Wikipedia: Present value of an annuity
  4. Fundamentals of Financial Management (15th ed.) by Brigham, E. F., & Houston, J. F.
  5. Brealey, Richard A., Stewart C. Myers, and Franklin Allen. Principles of Corporate Finance. 13th ed. McGraw-Hill Education, 2020.
  6. Ross, Stephen A., Randolph W. Westerfield, and Jeffrey Jaffe. Corporate Finance. 12th ed. McGraw-Hill Education, 2019.
  7. Wikipedia: Annuity (finance)
  8. Standard curriculum — A-Level Accounting / Finance