**Instructions:**

- Enter the initial investment, annual interest rate, number of years, and cash flow per year.
- Additionally, you can enter cash flows at different time periods (comma-separated).
- Click "Calculate Future Value" to calculate the future value and see the results.
- Click "Clear Results" to clear the results and chart.
- Click "Copy Results" to copy the result to the clipboard.
- See the calculation history below.

**Results:**

**Cash Flows Over Time:**

**Calculation and Explanation:**

**Calculation History:**

The future value of cash flows calculator is a useful financial tool for determining the future value of a series of cash flows given their periodic amount, number of periods, and interest rate. It is based on the concept of time value of money.

## Concept

The calculator uses the formula:

Future Value = CF [(1 + r)^n – 1] / r

Where:

CF = Cash flow per period

r = Periodic interest rate

n = Number of periods

This formula calculates the accumulated value of an annuity, which is a fixed sum of money paid periodically.

Each cash flow gets compounded by the interest rate over the number of periods. The sum of all such compounded cash flows gives the total future value.

## Features

Key features of the calculator:

- Accepts uneven cash flows over irregular periods
- Handles both payments and income streams
- Interest can be compounded annually, quarterly, etc.
- Adjustable compounding periods
- Flexible number of payment periods
- Graphical representation of cash flows
- Detailed amortization table and schedules

## Benefits

Benefits of using the future value calculator:

- Estimates growth of savings, investments, pensions
- Models loan repayments under different scenarios
- Analyzes profitability of financial instruments
- Plans for big future expenses like children’s education
- Compares relative outcomes of multiple options
- Simplifies complex time value of money calculations

## Applications

Typical applications include:

- Retirement planning and savings goals
- Evaluating annuities and sinking funds
- Capital budgeting and project management
- Modeling investment patterns
- Personal financial planning
- Forecasting cash flow streams

## Conclusion

The future value of cash flows calculator is a handy tool for easily estimating the time value of money. It lets users model both periodic payments and non-uniform income streams over long time horizons. The detailed cash flow schedules provide valuable insights for data-driven financial planning and decision making.

## References

- Bodie, Z., Kane, A., Marcus, A. J., & Mohanty, P. (2018). Investments. New York, NY: McGraw-Hill Education.