Calculate how much to save each month to reach a savings goal by a date, or how long a monthly deposit takes to get there, with interest.
Put aside $662.08 a month for 5 years to reach $50,000.00: $5,000.00 you already have, $39,724.61 of new deposits and $5,275.39 of interest.
| Year | Deposits | Interest | Balance |
|---|---|---|---|
| 1 | $7,944.92 | $351.00 | $13,295.92 |
| 2 | $7,944.92 | $688.98 | $21,929.82 |
| 3 | $7,944.92 | $1,040.74 | $30,915.49 |
| 4 | $7,944.92 | $1,406.83 | $40,267.24 |
| 5 | $7,944.92 | $1,787.84 | $50,000.00 |
The denominator is the value of 60 deposits of 1.
The monthly deposit needed is what closes the gap between the goal and what your current savings will grow to: C = (G − S(1 + i)^n) ÷ (((1 + i)^n − 1) ÷ i), where G is the goal, S the amount already saved, i the monthly rate and n the number of months. In the other mode, the number of months comes from logarithms of the same equation and is rounded up to the month in which the goal is reached.
With the defaults, reaching 50,000 in 5 years from 5,000 already saved at 4% a year takes 662.08 a month. The 60 deposits add up to 39,724.61, and interest supplies the remaining 5,275.39 on top of the 5,000 you started with.
Interest is compounded monthly at a fixed rate, with deposits at the end of each month unless you choose the start under More options. Tax on interest and changes in the rate are not included.
Checked against: Python decimal: (50000 − 5000·(1+0.04/12)^60) / (((1+i)^60 − 1)/i) = 662.0768…; same as Excel =PMT(4%/12,60,-5000,50000)
Checked against: Python decimal, annuity-due factor: 659.8772…
Checked against: 12000 / 12 by definition
Checked against: Starting balance exceeds the goal, so no deposit is needed
Subtract what your current savings will grow to from the goal, then divide by the annuity factor ((1 + i)^n − 1) ÷ i. To reach 50,000 in 5 years from 5,000 at 4% compounded monthly, you need 662.08 a month; Excel's =PMT(4%/12, 60, -5000, 50000) gives the same. With no interest the same goal takes (50,000 − 5,000) ÷ 60 = 750 a month.
Solve the savings equation for the number of months and round up. Starting from 5,000 and saving 500 a month at 4%, the balance first passes 50,000 in month 77, after 6 years 5 months; raising the deposit to 750 cuts that to 54 months. Excel's NPER function solves the same equation.
More the longer the horizon. Over 5 years, 4% interest cuts the deposit needed for 50,000 from 750 to 662.08 a month, and 5% cuts it to 640.87. Over 10 years at 4%, the deposit falls to 288.94 a month and interest supplies 10,327.63 of the 50,000.
Slightly: a deposit made at the start of the month earns one extra month of interest. For 50,000 in 5 years from 5,000 at 4%, the deposit needed is 659.88 at the start of each month against 662.08 at the end, a difference of 2.20 a month.
Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 6 worked examples whose answers come from independent sources; for example, “50,000 in 5 years from 5,000 at 4%” is checked against Python decimal: (50000 − 5000·(1+0.04/12)^60) / (((1+i)^60 − 1)/i) = 662.0768…; same as Excel =PMT(4%/12,60,-5000,50000).
Microsoft Excel PMT function; Microsoft Excel NPER function.
For planning only. Lenders, tax authorities and markets apply their own rounding, fees and rules; confirm figures with them before you commit.
6 worked examples with independently sourced answers ship with this calculator. They run in the test suite; you can run them here too.
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