FinanceTime Value of MoneyUniversity

Present Value of a Single Sum Calculator

Determines the current value of a single future lump sum amount, discounted at a specified interest rate over a number of periods.

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Present Value

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Overview

The present value of a single sum calculates what a future amount of money is worth today, considering that money has earning potential over time. This concept, known as the time value of money, acknowledges that a dollar today is worth more than a dollar in the future due to its capacity to be invested and earn a return. It involves 'discounting' a future value back to the present using an appropriate interest rate, also known as the discount rate.

Symbols

Variables

PV = Present Value, FV = Future Value, r = Interest Rate (per period)

Present Value
Future Value
Interest Rate (per period)

Apply it well

When To Use

When to use: This equation is applied when you need to determine the current worth of a single future payment or receipt. It is crucial for evaluating investment opportunities, comparing a future payout to a current investment, and making informed financial decisions. Additionally, it's used in financial planning for future goals like retirement or education, and for valuing assets, loans, or liabilities that involve a single future cash flow.

Why it matters: The Present Value of a Single Sum is a fundamental concept in finance because it allows for the comparison of cash flows occurring at different points in time, enabling rational financial decision-making. It quantifies the 'time value of money,' recognizing that money available today is more valuable than the same amount in the future due to factors like inflation, opportunity cost, and risk. Understanding this principle helps individuals and businesses make informed choices about investments, savings, and loans.

Avoid these traps

Common Mistakes

  • Using an inconsistent time unit for the interest rate and the number of periods (e.g., an annual rate with monthly periods without proper adjustment).
  • Failing to correctly adjust the interest rate and number of periods for compounding frequencies other than annual (e.g., semi-annual, quarterly, or monthly compounding).

One free problem

Practice Problem

What is the present value of $10,000 to be received in 5 years, if the discount rate is 8% compounded annually?

Present Value10000
Future Value0.08
Interest Rate (per period)5

Solve for:

Hint: Use the formula PV = FV / (1 + r)^n.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Brealey, R. A., Myers, S. C., & Allen, F. (Year). Principles of Corporate Finance. McGraw-Hill Education.
  2. Corporate Finance Institute. (n.d.). Time Value of Money. Retrieved from Corporate Finance Institute website.
  3. Finance Strategists. (2023, March 29). Present Value of a Single Amount. Retrieved from Finance Strategists website.
  4. Standard Financial Mathematics Principles
  5. Commonly found in introductory finance and economics textbooks (e.g., Principles of Corporate Finance by Brealey, Myers, and Allen; Fundamentals of Financial Management by Brigham and Houston)