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.
Excel equivalent
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)
| 10 years |
