**Instructions:**

- Enter the Future Value, Discount Rate, Number of Years, and Compounding Frequency.
- Click "Calculate" to calculate the Present Value and display it in the chart and result below.
- Your calculation history will be shown in the table below the calculator.
- Use "Clear" to reset the calculator and "Copy Result" to copy the present value to the clipboard.

**Calculation History**

Calculation | Present Value |
---|

**Concepts**

Present value (PV) is the value of a future sum of money today. It is calculated by discounting the future sum of money by a discount rate, which is the rate of return that can be earned on an investment.

The basic present value formula is as follows:

```
PV = FV / (1 + r)^n
```

Where:

- PV is the present value
- FV is the future value
- r is the discount rate
- n is the number of periods

**Formulae**

The following formulae can be used to calculate the present value of different types of cash flows:

**Single cash flow:**- PV = FV / (1 + r)^n

**Annuity:**- PV = A * [1 – (1 + r)^-n] / r
- Where A is the annual payment

**Perpetuity:**- PV = A / r

**Benefits**

There are a number of benefits to using a basic present value calculator:

- It can help you to make informed financial decisions. For example, you can use a present value calculator to compare the value of different investment options or to determine how much you need to save to reach a financial goal.
- It can help you to avoid overpaying for assets. For example, if you are considering buying a house, you can use a present value calculator to determine the maximum amount that you should offer, based on the expected future cash flows from the property.
- It can help you to understand the value of time. For example, you can use a present value calculator to see how the value of a future sum of money decreases over time due to inflation.

**Interesting facts**

- The concept of present value has been around for centuries. It was first used by merchants in the Middle Ages to calculate the value of bills of exchange.
- Present value is a fundamental concept in finance and economics. It is used to evaluate a wide range of financial assets and liabilities, including bonds, loans, stocks, and real estate.
- Present value is also used in other fields, such as actuarial science and project management.

**References**

**Financial Mathematics: An Introduction**by Irvin H. Siegel and John W. Van Horne (2013)**Investments**by Zvi Bodie, Alex Kane, and Alan J. Millerron (2018)**Corporate Finance**by Richard Brealey, Stewart Myers, and Frank Allen (2016)

**Examples**

The following table shows some examples of present value calculations:

Cash flow type | Future value | Discount rate | Number of periods | Present value |
---|---|---|---|---|

Single cash flow | $10,000 | 5% | 5 years | $7,835 |

Annuity | $1,000 | 5% | 5 years | $4,329 |

Perpetuity | $1,000 | 5% | – | $20,000 |

**Applications**

Basic present value calculators can be used for a variety of applications, including:

**Investment analysis:**Investors can use present value calculators to compare the value of different investment options and to determine the expected return on an investment.**Loan analysis:**Borrowers can use present value calculators to determine the monthly payments on a loan and to determine the total cost of a loan.**Financial planning:**Individuals and families can use present value calculators to develop financial plans and to reach their financial goals.

**Conclusion**

Basic present value calculators are a valuable tool for anyone who wants to make informed financial decisions. They can be used to compare the value of different investment options, to determine the monthly payments on a loan, and to develop financial plans.