How this calculator works
A savings goal has four moving parts: the target, what you start with, the return your money earns and the time available. Change any three and the fourth follows. In deposit mode the calculator holds the date fixed and solves for the deposit that reaches the target, including interest on the starting balance and on each deposit. In time mode it holds the deposit fixed and solves for the number of periods. Deposits are assumed to be level and to land at the same point in every period, either the start or the end. Interest compounds at the same frequency as the deposits, which is a simplification: a real account may compound daily while you deposit monthly, and the difference is small but not zero. The annual rate is nominal, so a 5% rate compounded monthly means 5% / 12 each month. The inflation figure does not change the projection; it re-expresses the goal in today's money so you can judge whether the target still buys what you intend.
Formula
Let i = annual rate / periods per year and n = periods. Balance = P(1+i)^n + D((1+i)^n - 1)/i, where P is the starting balance and D the deposit; with deposits at the start of each period, multiply the deposit term by (1+i). Deposit needed D = (G - P(1+i)^n) x i / ((1+i)^n - 1). Time n = ln((G + D/i) / (P + D/i)) / ln(1+i). At a zero rate, D = (G - P)/n and n = (G - P)/D. Goal in today's money = G / (1 + inflation)^(years).
Worked example
A $20,000 goal in five years from a $2,000 start at 5% compounded monthly needs $256.35 a month when deposits land at the end of each month. The 60 deposits total $15,380.93, so contributions including the starting amount are $17,380.93 and interest is $2,619.07. Paying $250 a month instead reaches the goal in 61.30 months, just over five years. At 2.5% inflation, $20,000 in five years is worth $17,677.09 today.
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Frequently asked questions
Should the deposit go in at the start or the end of the period?
Use the start if the money leaves your account on the first day and earns interest for the whole period. Use the end if it leaves on the last day. The difference is one period of interest on each deposit, which is small per period but adds up over years.
Does a higher return always help?
For the arithmetic, yes. In practice a higher expected return comes with more risk and more variability, and savings for a short-term goal are usually held in low-risk accounts. Do not assume an equity return for money you need within a year or two.
Why does the inflation figure not change the deposit?
Inflation changes what the money buys, not how many dollars are needed to reach a stated dollar target. It is shown so you can see the goal in today's money and decide whether to raise the target.
Can I include an employer match or a grant?
Add it to the deposit, or model it separately and add the two balances. A match is usually a percentage of your contribution, so the effective deposit changes with your salary and the plan rules.
What if I miss a deposit?
The projection assumes every deposit is made on time. A missed deposit costs its own interest and everything that interest would have earned, so catching up later requires a larger payment. Recalculate with the new starting balance after any gap.