Present Value (Single Sum, Discrete Compounding) Calculator
Calculates the present value of a single future sum discounted at a discrete rate over a specified number of periods.
Formula first
Overview
This equation represents the foundational concept of discounted cash flow analysis, determining what a future payment is worth in today's currency. By dividing the future value by the compounding growth factor, it accounts for the opportunity cost of capital and the time value of money. It assumes that interest is credited at discrete intervals, such as annually or monthly.
Symbols
Variables
PV = Present Value, FV = Future Value, r = Interest Rate per Period, n = Number of Periods
Apply it well
When To Use
When to use: Apply this when you need to determine the current worth of a specific cash inflow or outflow expected at a known future date given a constant discount rate.
Why it matters: It is the core mechanism behind bond pricing, investment appraisal, and capital budgeting, allowing investors to compare the value of money across different time horizons.
Avoid these traps
Common Mistakes
- Using an annual interest rate when compounding is performed on a sub-annual basis without adjusting the period count.
- Confusing the nominal interest rate with the effective periodic rate.
- Neglecting to adjust the number of periods when the compounding frequency changes.
One free problem
Practice Problem
What is the present value of $5,000 received in 3 years at an annual interest rate of 5%?
Solve for:
Hint: Divide 5000 by 1.05 raised to the power of 3.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Brealey, R. A., Myers, S. C., & Allen, F. (2020). Principles of Corporate Finance.
- Ross, S. A., Westerfield, R. W., & Jaffe, J. (2019). Corporate Finance.