A common question that present value addresses is “how much money do I need right now to have a savings goal in the future?”
Present value of a single sum
Present value of a series of payments
Present Value = Future Value ÷ (1 + Rate of Return)Number of Periods
- “Future Value” is a sum of money in the future.
- “Rate of return” is a decimal value rate of return per period (the calculator above uses a percentage). A return of “2.2%” per year would be calculated as “0.022.”
- “Number of Periods” are the number of compounding periods.
What is the present value of $2,000, 10 years from now, assuming a 2.2% annual rate of return?
Present Value = 2000 ÷ (1 + 0.022)10
Present Value = 2000 ÷ 1.02210
Present Value = 2000 ÷ 1.243108
Present Value = 1,608.87
What is the present value of $1000, 48 months from now, assuming a 1% monthly rate of return?
Present Value = 1000 ÷ (1 + 0.01)48
Present Value = 1000 ÷ 1.0148
Present Value = 1000 ÷ 1.612226
Present Value = 620.26
Present Value Table
What is the difference between future value (FV) and present value (PV)?
Future value is the value of money at a future date, and present value is the value at today’s date.
A common question for future value is “in 10 years, what will $2,000 in today’s money invested at a rate of 4% be worth?.”
What is the difference between net present value (NPV) and present value (PV)?
Net Present Value is the present value of more than one future sums of money. Present value is for only one future sum of money.
A net present value can combine multiple calculations to find the present value of future values (e.g. $5,000 10 years from now), annuity streams (e.g. $400/month for 48 months), and perpetuities (e.g. $5 daily in perpetuity).
- Wikipedia – Present Value & Time Value of Money – Wikipedia’s entries on present value. Present value is a calculation within the concent of time value of money.
- Accounting Coach – Present Value of a Single Amount – A more detailed description of how the present value of a future sum is derived.
- Math is Fun – Present Value – Another more detailed description of the present value and how it is calculated.
- Khan Academy – Introduction to Present Value & Present Value 2 – A video introduction to present value from Khan Academy, a provider of free learning and tutorial videos.
- The Theory of Interest by Irving Fisher – 1930s book in public domain detailing the concept of interest. One of the first books detailing the concept of interest and how it is calculated.
- Concise Encyclopedia of Economics – Present Value by David R. Henderson – An explanation of present value from David R. Henderson of Stanford University’s Hoover Institution.
- StudyFinance.com by Dr. Sharon Garrison – Time Value of Money and Present Value – A simple explanation of time value of money and present value from the University of Arizona’s Dr. Sharon Garrison.