The savings-goal formula
The starting balance grows on its own; the rest must come from monthly deposits. Solving the future-value-of-an-annuity equation for the payment gives:
Where i is the monthly rate (annual ÷ 12), n is the number of months, Start is today's balance and Goal is the target. If the rate is zero it simplifies to (Goal − Start) ÷ n.
Worked example
Goal $20,000 in 36 months, starting at $2,000, earning 4%:
Saving smarter
Two levers change the monthly figure most: time and rate. Doubling the months roughly halves the required deposit, and a higher yield (a high-yield savings account or money-market fund) lets your interest do more of the work. Automating the transfer the day you're paid is the single most reliable way to actually hit the goal.