Savings goal
Turn a target balance into a monthly deposit. The engine grows what you already have first, then solves the sinking-fund formula for the shortfall — so the number it returns is the amount new saving has to cover.
| Year | Contributed | Balance | Share of goal |
|---|---|---|---|
| Year 1 | $4,546 | $8,793 | 29.3% |
| Year 2 | $9,092 | $13,782 | 45.9% |
| Year 3 | $13,638 | $18,973 | 63.2% |
| Year 4 | $18,184 | $24,377 | 81.3% |
| Year 5 | $22,730 | $30,000 | 100.0% |
Contributed is cumulative cash in. The gap between it and the balance is investment growth — zero if the rate is zero.
FV = PV(1+i)ⁿ + PMT[(1+i)ⁿ−1]/i · sinking-fund form
PMT = [FV − PV(1+i)ⁿ]·i/[(1+i)ⁿ−1] · solve for the deposit
PMT = gap/n · the degenerate case
FV − PV − n·PMT · what compounding contributed
A clear path from inputs to results.
A savings goal is a sinking-fund problem: grow what you already have, then solve for the deposit that closes the gap. Doing it in that order matters, because the growth on the starting balance can be a large part of the answer over long horizons.
How to use
- Enter the target balance.
- Add what you have already saved toward it.
- Set the deadline in years.
- Choose an expected return appropriate to the horizon.
- Read the required monthly deposit and the split between contributions and growth.
The formula
Reference: Standard sinking-fund formula (Broverman, Mathematics of Investment and Credit).
Worked example
$30,000 goal in five years from $4,000 at 4%
- Target $30,000.
- Already saved $4,000.
- Five years at 4%.
- 1
Monthly rate 0.3333%, 60 months.
- 2
Starting balance grows to 4,000 × 1.003333^60 = $4,884.
- 3
Gap: 30,000 − 4,884 = $25,116.
- 4
Deposit: 25,116 × 0.003333 / (1.003333^60 − 1) = $378.83 a month.
- 5
Total contributions $22,730; growth contributes the remaining $3,270.
$378.83 a month for 60 months, of which about $3,270 is investment growth.
Interpreting the result
At a 4% return, growth covers roughly a quarter of the goal. At 0% the deposit is simply the gap divided by the months — $418.60 here. The difference is the reward for the return assumption, and it comes with the risk that the return does not arrive.
Assumptions & limitations
- Contributions are made at month end and the return is constant.
- The return assumption is realistic for the horizon: cash-like for under three years, diversified for longer.
- No fees are deducted; a 1% fee would raise the required deposit.
- The target is in nominal currency, not inflation-adjusted.
Frequently asked questions
What return should I assume for a short goal?
For goals inside three years, use a savings account or short-duration bond rate. Equities can fall 30% in a year, which turns a two-year goal into a missed deadline.
Should I save monthly or in a lump sum?
Monthly matches how income arrives and removes timing decisions. If you have the cash already, investing it earlier generally wins over spreading it out.
Why does the monthly amount fall so much with a longer deadline?
Because you have more months to contribute and more time for compounding. Stretching from three to five years typically cuts the deposit by about 40%.
How do I handle inflation?
Raise the target by expected inflation over the horizon, or use a real return and a real target. Mixing nominal returns with a nominal target and then complaining about prices is the common error.
Methodology last reviewed 2026-10-18. Results are informational and not financial or engineering advice — see our disclaimer.