You can use the natural logarithm (LN) to work out the length of time it takes to achieve a unit of growth, such as with compound interest.

LN returns the natural logarithm of a number, based on the constant *e*. This function is the inverse of the EXP function, which raises e to the nth power.

In terms of measuring growth:

- EXP allows you to enter time in order to work out growth
- LN allows you to enter growth in order to work out the time it would take to achieve that growth

## Syntax

`LN(Number)`

## Arguments

Argument | Data type | Description |

Number | Numeric line item, property or expression | Number you want to return the natural logarithm for |

**Syntax example**

Here's an example of how to use LN to find out how long it will take to achieve a specific amount of growth based on compound interest.

- If an investment grows at a rate of 10% per annum how long will it take for the investment to reach a specific amount?

To calculate this, use this syntax:

`LN(total amount after growth/current amount )/LN(percentage growth rate represented as a multiplier e.g. 1.10 for 10% in this instance)= Time to hit the specific amount`

## Constraints

You can only use LN with positive numbers.

## Excel equivalent

## Related Anaplan functions

**Example**

Using the example above, let's work out how long it will take for an initial investment of $25,000 to reach $65,000.

LN(total amount after growth/current amount )/LN(interest rate represented as a multiplier)= Time in years to hit the specific amount

LN($65,000/$25,000)/LN(1.10)=10.0252821576 (approximately 10 years).

Initial investment | $25,000 |

Investment goal | $65,000 |

Annual percentage rate (APR) | 10% |

Time to hit goal (using LN)
| 10 years |