To calculate how many months it will take to fully fund your emergency fund by only putting 50% of your discretionary money toward it, you will need to take the total amount needed for your emergency fund and divide it by the amount you plan to contribute each month.
Assuming you have the total you are aiming for in your emergency fund (let’s call it X) and your discretionary monthly contribution is Y, then you will contribute 0.5Y (which is 50% of your discretionary money).
The formula you would use is: \[ \text{Months} = \lceil \frac{X}{0.5Y} \rceil \] where \( \lceil \text{value} \rceil \) represents rounding up to the next whole number.
If you provide the values of X and Y, I can help you calculate the exact number of months.