How this number is made
A savings goal is either a date problem or a payment problem. If you know what you can set aside, solve for time. If you know the date — a lease, a tuition bill, a move — solve for the monthly amount. Interest helps, but a 4% yield will not rescue a deposit that is too small.
- Pick the mode before you trust the headline. The hidden field is not part of the math.
- Keep the return boring if the money has to be there on a date. Emergency funds are not a place for a stock assumption.
- Subtract what you have already saved so you are not funding the same dollar twice.
Formula
With monthly rate r, months n satisfy goal = current × (1+r)^n + deposit × ((1+r)^n − 1) ÷ r. The payment mode solves that equation for the deposit.
Worked example
A $10,000 emergency fund with $1,500 already saved and $250 a month at 4% takes a bit under three years. Stretch the date to three years exactly and the required deposit falls. Both answers are the same equation run in opposite directions.
Questions
Should an emergency fund earn a market return?
Only if you can watch it fall and still pay the emergency. Many people use a savings account or Treasury fund and type a smaller rate. The calculator will not scold you either way.
What if I save nothing some months?
The model assumes every month happens. Missed months push the date out by about a month plus the interest you did not earn. There is no streak bonus.