Time Value of Money Calculator
Convert one lump sum between present value and future value using a nominal annual rate, term, and compounding frequency.
Inputs
Live results
Value over time
Annual value schedule
| Year | Opening value | Growth during year | Closing value |
|---|
How to use the Time Value of Money Calculator
What this calculator does
This calculator converts one lump sum between present value and future value. It applies a nominal annual interest or discount rate for a specified term and compounding frequency. Use it to answer either “What could this amount become?” or “What amount today is equivalent to a future amount?” It does not model recurring deposits, taxes, fees, inflation, investment volatility, changing rates, or the probability that an expected return will actually occur.
When to use it
Use it when comparing cash available now with a promised future payment, estimating the future balance of a single deposit, discounting a project's one-time future receipt, or checking how compounding frequency changes a quoted nominal rate. The underlying principle is explained in the open textbook section on time value of money basics.
How to calculate
- The calculator opens with a ready-to-use demonstration: Future value, $10,000 present value, 6.5% annual interest, 10 years, and monthly compounding. Its Excel workbook is available immediately.
- Choose Solve for: Future value compounds the starting amount forward; Present value discounts the entered future amount backward.
- Replace the Present value or Future value, Interest rate, Term, and Compound frequency. Results, chart, and schedule update live.
- Read the main answer and supporting measures, then use Download Excel to export the current validated model. Reset clears the demonstration and results; Excel export stays disabled until a complete valid state is entered again.
Input guide
Solve for is required and accepts Future value or Present value. Future value means the entered amount is today's value; Present value means the entered amount is the future target. Switching direction changes the formula but preserves the economic assumptions.
Present value or Future value is a required nonnegative U.S.-dollar amount. Enter digits with an optional decimal point and comma grouping, such as 10,000. Do not use decimal commas or scientific notation. A larger amount scales every dollar result proportionally.
Interest rate is the required nominal annual percentage rate, from -99.99% through 1,000%, such as 6.5. Negative rates reduce future value and increase the present amount needed for a fixed future value. A common mistake is entering 0.065 for 6.5%; enter 6.5 instead.
Term is required in years, greater than 0 and no more than 200. Decimals are accepted, so 2.5 means two and a half years. Longer terms magnify compounding or discounting. Do not enter months directly; convert months to years, such as 18 months = 1.5 years.
Compound frequency is required. Choose Yearly, Semi-annually, Quarterly, Monthly, Weekly, Daily, or Continuous. More frequent compounding usually raises future value when the nominal rate is positive. Continuous compounding uses the exponential formula rather than a finite number of periods.
Output guide
Future value or Present value is the primary calculated lump sum in dollars. Starting amount identifies the entered cash amount. Total growth is future value minus present value, so it may be negative under a negative rate. Effective annual rate converts the selected nominal rate and frequency into one annual growth rate. Compounding periods is the total number of finite crediting periods; continuous compounding is labeled Continuous.
The Annual value schedule shows Year, Opening value, Growth during year, and Closing value. The chart plots the same closing-value series. These are model estimates, not guaranteed investment returns. A zero rate produces no growth, while a negative rate produces a declining line.
Worked example
With $10,000 today, a 6.5% nominal annual rate, monthly compounding, and a 10-year term, the periodic rate is 0.065 ÷ 12. The calculator applies 120 monthly periods: $10,000 × (1 + 0.065 ÷ 12)120 = $19,121.84. Total growth is $9,121.84, and the effective annual rate is approximately 6.70%. These values match the first-open controls, schedule, chart, and workbook.
How the model works
For finite compounding, future value equals present value multiplied by (1 + r ÷ n)n×t, where r is the annual rate as a decimal, n is compounding periods per year, and t is years. Present value divides future value by the same growth factor. For continuous compounding, the growth factor is er×t. OpenStax provides a detailed walkthrough of methods for solving TVM problems.
Interpretation and limitations
Compounding frequency matters because a quoted nominal rate is divided across more crediting periods. The SEC's Investor.gov compound interest resource also illustrates how frequency affects growth. For real decisions, use a rate that reflects the risk and timing of the cash flow. A discount rate is not automatically the same as inflation, a savings-account APY, or an investment's expected return.
This tool handles one cash flow at one future date. A stream of payments requires an annuity or discounted-cash-flow model. Also remember that nominal projections do not show purchasing power after inflation and do not account for tax, fees, default risk, or market variability.