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.
By AdminDrafted with AI writing toolsUpdated Checked examples: 6
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.
Grow what you have already saved to the deadline, subtract it from the goal, and divide the gap by the deposit factor ((1 + i)^n − 1) ÷ i, where i is the annual rate ÷ 12 and n the number of months. Reaching 50,000 in 5 years from 5,000 at 4% takes 662.08 at the end of each month.
As a formula, the deposit is C = (G − S(1 + i)^n) ÷ (((1 + i)^n − 1) ÷ i), with G the goal and S the amount already saved. Interest is compounded monthly at one fixed rate.
The 60 deposits total 39,724.61, and interest supplies the other 5,275.39 on top of the 5,000 you started with.
With no interest, the same goal takes (50,000 − 5,000) ÷ 60 = 750 a month, so 4% interest saves 87.92 a month.
Excel's PMT function gives the same answer: =PMT(4%/12, 60, -5000, 50000) returns −662.08, the minus sign marking money you pay in.
A deposit made on the first of the month earns one more month of interest, so the deposit needed is slightly smaller. Default is the example above, Start deposits moves each deposit to the start of the month, and Zero rate removes interest:
| Scenario | Monthly deposit needed |
|---|---|
| Default | 662.08 |
| Start deposits | 659.88 |
| Zero rate | 750.00 |
The timing is worth 2.20 a month here. At a zero rate it makes no difference, because no interest is earned either way.
Interest matters more the longer the horizon. For the 50,000 goal with 5,000 saved, 4% cuts the 5-year deposit from 750 to 662.08 a month, and 5% cuts it to 640.87.
Over 10 years the same goal needs 375 a month with no interest and 288.94 at 4%, when interest supplies 10,327.63 of the 50,000.
Hold the deposit fixed and count the months until the balance first reaches the goal: n = ln((G + C/i) ÷ (S + C/i)) ÷ ln(1 + i), rounded up to a whole month.
Saving 500 a month from 5,000 at 4% passes 50,000 in month 77, after 6 years 5 months, with 50,269.70 in the account. Raising the deposit to 750 cuts the wait to 54 months.
Because the count rounds up, the final balance usually lands a little above the goal. With no deposits at all, 5,000 at 4% still reaches 6,000 in 55 months, while a goal you cannot reach without deposits or interest has no answer.
The rate is an assumption, not an account offer or a forecast. Tax on interest, account fees, withdrawals and rate changes are left out, so use an after-tax rate if your interest is taxed.
When the final balance is the unknown instead of the deposit or the time, use the compound interest calculator.
Checked against: (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: Independent calculation
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.
For planning only. Lenders, tax authorities and markets apply their own rounding, fees and rules; confirm figures with them before you commit.
This calculator includes 6 worked examples with independently sourced answers. They run in the test suite, and you can run them here too.