Use the natural logarithm (LN) to work out the length of time it takes to achieve a unit of growth.

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.

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(1 + 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.

LN

## 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(1 + interest rate represented as a multiplier)= Time in years to hit the specific amount

LN($65,000/$25,000)/LN(1 + 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)  LN(Investment goal/Initial investment)/LN(1 + 'Annual percentage rate(APR)') 10 years

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