How to Use
Enter the Future Value, the amount you expect to receive or pay in the future.
Enter the Annual Discount Rate as a percentage (e.g. 5 for 5%).
Enter the Time Period in years.
Choose a Compounding Frequency: annual, semi annual, quarterly, or monthly.
Optionally enter a Periodic Payment to calculate the present value of an annuity stream as well.
Click Calculate to see the present value, discount amount, and a table broken down by year.
How Present Value Works
Present value answers one question: how much is a future sum worth in today's money? Money today is worth more than the same amount later because it can be invested to earn a return. The formula is PV = FV / (1 + r)^n, where FV is the future value, r is the discount rate per compounding period (annual rate divided by periods per year, divided by 100), and n is the total number of periods. For an annuity, a series of equal periodic payments, the formula becomes PV = PMT x [1 - (1+r)^(-n)] / r. A higher discount rate produces a lower present value, reflecting greater time preference or risk. Compounding frequency changes r and n: monthly compounding divides the annual rate by 12 and multiplies years by 12, causing faster discounting than annual compounding at the same nominal rate.
Worked Example
- Goal: find the present value of 10,000 received in 5 years at a 6% annual discount rate, compounded annually.
- r = 6 / 1 / 100 = 0.06 | n = 5 x 1 = 5 periods
- PV = 10,000 / (1 + 0.06)^5 = 10,000 / 1.3382 = 7,472.58
- Discount amount = 10,000 minus 7,472.58 = 2,527.42 | Discount % = 25.27%
- Now add a 500 annual annuity payment: PV_annuity = 500 x [1 minus (1.06)^(-5)] / 0.06 = 2,106.18
- Total PV = 7,472.58 + 2,106.18 = 9,578.76
When to Use This Calculator
- Valuing a bond, investment, or contract that pays out in the future
- Comparing a lump sum payout today versus an annuity stream over time
- Evaluating whether a project's future returns justify today's cost
- Discounting expected future cash flows for a business valuation (DCF)
- Understanding how inflation or opportunity cost reduces the value of future money
- Finance coursework or exam preparation involving time value of money
Important Note
This calculator assumes a constant discount rate and ignores taxes, inflation adjustments, credit risk, and transaction costs. The discount rate you choose greatly affects the result. A small change in rate produces a large difference in present value over long time horizons. For investment or financial planning decisions, consult a qualified financial advisor.
Higher vs. Lower Discount Rate
Key Features
Lump Sum and Annuity Support
Calculate the present value of a single future payment, a series of equal periodic payments, or both combined in one result.
Flexible Compounding
Choose annual, semi annual, quarterly, or monthly compounding to match the actual terms of your investment or loan.
Discount Table by Year
See the discount factor and present value for every year up to 50, so you can trace exactly how time reduces value.
Interactive Chart
A line chart plots present value against each year, making the exponential decay of future money immediately visible.
Frequently Asked Questions
What discount rate should I use?
The discount rate depends on context. For risk free comparisons, use a government bond yield. For business valuations, use the weighted average cost of capital (WACC). For personal decisions, your expected rate of return on alternative investments works well.
Does compounding frequency matter much?
Yes, especially at higher rates and longer time horizons. Monthly compounding applies a smaller rate more often, which compounds faster. The difference between annual and monthly compounding on a 10% rate over 20 years is meaningful.
What is the difference between present value and net present value?
Present value discounts a single future cash flow or annuity stream. Net present value (NPV) sums the present values of multiple cash flows, including the initial investment cost, which is usually negative. NPV tells you whether a project adds or destroys value overall.