Savings goal calculator

What this number means

This is the monthly amount that, added to what you already have and growing at the rate you entered, reaches your target on the date you set.

The split beneath it is worth looking at. The contributed by interest figure is what the compounding does rather than you, and it is the argument for starting earlier: extend the horizon and that share grows disproportionately, because the early contributions have the longest to work.

This page will not tell you whether the goal is realistic or whether the money is better used elsewhere. It answers the arithmetic question you asked.

How this is calculated

From the future value of an annuity due, rearranged for the payment:

• FV = P(1+i)^n + C x [((1+i)^n - 1) / i] x (1+i)
• where P is what you have now, C the monthly contribution, i the monthly rate and n the number of months.
• Solving for C gives the shortfall, target less what your existing balance grows to, divided by the annuity factor.

The trailing (1+i) is the part that gets skipped. It is what makes this an annuity due: contributions land at the start of each period and earn that period's interest. Without it you have an ordinary annuity, where payments land at the end, and the required contribution comes out slightly higher. Most calculators do not say which they use.

At a zero rate the general form divides by zero, so it degenerates to the shortfall divided by the number of months, which is handled separately.

No regulator defines this calculation. It is the standard annuity formula from financial mathematics, and saying so is more useful than pointing at an agency that does not govern it. Where a rule does apply on this site we name it: the APY page follows Regulation DD, and the credit card pages follow Regulation Z.

So the arithmetic here is checkable and the assumptions are ours. They are listed above and under the limits below, and the two conventions that matter, when money moves and how interest rounds, are stated rather than left for you to infer.

What this does not account for

• Inflation. The target is in today's dollars. If what you are saving for gets more expensive, the real target is higher.
• Returns that vary. A fixed rate is right for a savings account or a CD and wrong for investments, where the sequence of returns matters as much as the average.
• Tax on the interest as it is earned, which reduces the effective rate.
• Contributions that change. This assumes the same amount every month, and most people's capacity to save moves.
• Employer matching or other contributions, which if present make the required figure lower.

Questions

What rate should I use?

For a goal within a few years, use what a savings account or CD is actually paying, because the money should not be at risk over a short horizon. For a goal ten or more years out, people commonly use a long-run investment assumption, but then the answer is an estimate rather than a plan: real returns vary year to year and a bad sequence near the end matters more than the average.

Should I subtract inflation from the rate?

If your goal is a thing whose price rises, yes. A 40,000 dollar car in five years will not cost 40,000 then. Entering a rate reduced by your inflation assumption gives you an answer in today’s money, which is usually what you actually want.

Why is the contribution lower than the target divided by the months?

Because the interest does part of the work. The gap between the two is exactly what the compounding contributes, and it grows with the rate and the horizon. On a short goal at a low rate the two figures are almost identical.

What if I cannot manage the monthly figure?

The three levers are the amount, the date and the starting balance. Pushing the date out is usually the most powerful of the three, because it adds both contributions and compounding. This page will show you what each change does; it will not tell you which to pull.