FinanceTime Value of MoneyA-Level
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Present Value (Single Sum) Calculator

Current worth of a future sum.

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Present Value

Formula first

Overview

The Present Value formula determines the current worth of a specific sum of money to be received in the future, adjusted for a specific rate of return. It reflects the fundamental principle that money available now is worth more than the same amount in the future due to its potential earning capacity.

Symbols

Variables

PV = Present Value, FV = Future Value, r = Interest Rate, n = Periods

Present Value
$
Future Value
$
Interest Rate
Periods

Apply it well

When To Use

When to use: Apply this formula when you need to evaluate the current value of a single future cash inflow or outflow. It is essential for comparing investment opportunities with different time horizons or assessing the impact of inflation and opportunity costs on future sums.

Why it matters: This concept is the bedrock of modern finance, enabling discounted cash flow analysis and net present value calculations. It allows individuals and businesses to make rational 'apples-to-apples' comparisons between immediate costs and distant rewards.

Avoid these traps

Common Mistakes

  • Using integer percentage (5 instead of 0.05).
  • Confusing PV and FV.

One free problem

Practice Problem

An investor expects to receive a lump sum of $10,000 in 5 years. If the annual market interest rate is 6%, what is the value of this payment today?

Future Value10000 $
Interest Rate0.06
Periods5

Solve for:

Hint: Divide the future value by (1 + r) raised to the power of the number of years.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Principles of Corporate Finance by Brealey, Myers, Allen
  2. Wikipedia: Time value of money
  3. Wikipedia: Present value
  4. Brealey, R. A., Myers, S. C., & Allen, F. (2020). Principles of Corporate Finance (13th ed.). McGraw-Hill Education.
  5. Brigham, E. F., & Ehrhardt, M. C. (2017). Financial Management: Theory and Practice (15th ed.). Cengage Learning.
  6. Wikipedia: Time value of money (accessed 2023-10-27)
  7. Standard curriculum — A-Level Business / Finance