## Present Value of 1 Table

A Present Value of 1 Table, also known as a Present Value Interest Factor (PVIF) table, is a table that shows the present value interest factors for various combinations of interest rates (r) and time periods (n). It simplifies the process of calculating the present value of a single sum to be received in the future.

The PVIF is calculated using the formula:

PVIF = 1 / (1 + r)^n

Where:

- r is the discount rate
- n is the number of periods

The table typically has interest rates running down the first column and the number of periods running across the top row. The intersection of the interest rate row and the periods column gives the present value interest factor.

For example, if you want to find the present value of $1 to be received in 5 years at an interest rate of 5%, you would find the intersection of the 5% interest rate row and the 5-year column. The resulting factor can be used to calculate the present value of a future sum.

This table is often used in financial analysis and investment planning because it simplifies the calculation process by providing the present value interest factor without needing to perform the calculation for each unique situation.

Here’s an example of what a Present Value of 1 Table might look like (note that actual figures may vary depending on the accuracy of calculation):

r/n | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

1% | 0.990 | 0.980 | 0.971 | 0.961 | 0.951 |

2% | 0.980 | 0.961 | 0.942 | 0.924 | 0.906 |

3% | 0.971 | 0.943 | 0.915 | 0.888 | 0.863 |

4% | 0.962 | 0.925 | 0.889 | 0.855 | 0.822 |

5% | 0.952 | 0.907 | 0.864 | 0.823 | 0.784 |

## Example of a Present Value of 1 Table

Suppose you are expecting to receive $10,000 in 5 years, and you want to determine the present value of this amount. Let’s use a discount rate of 5% per annum for the calculation.

Now, instead of using the PVIF formula directly, you can look up the factor in the Present Value of 1 Table.

For the intersection of 5% interest rate row and the 5-year column, the factor is 0.784 (assuming the table is rounded to three decimal places for simplicity).

Using this factor, you can find the present value of the $10,000 to be received in 5 years:

PV = FV * PVIF

PV = $10,000 * 0.784

PV = $7,840

Therefore, the present value of $10,000 received 5 years from now at a 5% discount rate is approximately $7,840.

As you can see, using the Present Value of 1 Table (or PVIF table) can simplify the calculation process, especially when you are dealing with multiple time periods or rates.