A savings goal has four numbers: the target, what you have already, what you add each month, and the time. Give three and the calculator finds the fourth – either how long it takes at your monthly deposit, or how much to put aside each month to arrive by a date. Interest is added monthly at the yearly rate you enter, so you can see how much of the goal it pays for.
Example: a $20,000 down payment. You have $2,000 and can save $500 a month in an account paying 4%. After 34 months you have $20,209: 2 years and 10 months. You paid in $19,000; interest added $1,209.
Months to save $20,000 from $2,000
| Monthly deposit | No interest | 2% a year | 4% a year | 5% a year |
|---|---|---|---|---|
| 200 | 7 y 6 m | 6 y 11 m | 6 y 5 m | 6 y 2 m |
| 300 | 5 y 0 m | 4 y 9 m | 4 y 6 m | 4 y 5 m |
| 500 | 3 y 0 m | 2 y 11 m | 2 y 10 m | 2 y 10 m |
| 750 | 2 y 0 m | 2 y 0 m | 1 y 11 m | 1 y 11 m |
| 1,000 | 1 y 6 m | 1 y 6 m | 1 y 6 m | 1 y 6 m |
| 1,500 | 1 y 0 m | 1 y 0 m | 1 y 0 m | 1 y 0 m |
The numbers work in any currency: the same goal and deposits in euros, pounds or yen give the same months.
Monthly deposit to reach a goal from zero
| Goal | Time | No interest | 4% a year | 5% a year |
|---|---|---|---|---|
| 5,000 | 1 year | 417 | 409 | 407 |
| 10,000 | 2 years | 417 | 401 | 397 |
| 20,000 | 3 years | 556 | 524 | 516 |
| 50,000 | 5 years | 833 | 754 | 735 |
| 100,000 | 10 years | 833 | 679 | 644 |
The formulas
With i = the yearly rate ÷ 12 and deposits at the end of each month:
- Balance after n months: P(1 + i)ⁿ + D × ((1 + i)ⁿ − 1) ÷ i, where P is what you start with and D the monthly deposit.
- Months to the goal G: n = ln((G·i + D) ÷ (P·i + D)) ÷ ln(1 + i), rounded up to a whole month.
- Deposit to reach G in n months: D = (G − P(1 + i)ⁿ) × i ÷ ((1 + i)ⁿ − 1).
Use the rate you will actually keep: a savings account’s APY after tax on the interest, where it is taxed. Rates change, so for a long goal a cautious rate is safer than today’s best offer.
Three things that make goals easier
- Pay yourself first: an automatic transfer on payday works better than saving what is left at the end of the month.
- Inflation: prices rise while you save. For a goal you will buy in five years, raise the target by the inflation you expect.
- Windfalls: a tax refund or bonus put straight into the goal shortens it by months. The detail “With 100 more a month” shows what a small increase does.
To see a lump sum grow without deposits, use the compound interest calculator. Your figures stay on your device, and once zet4u is saved there, the calculator works offline too.
Frequently asked questions
How much do I need to save each month to reach $20,000 in 3 years?
$556 a month with no interest, or about $524 at 4% a year (interest added monthly). If you already have $2,000 put aside, it drops to about $465 at 4%.
How long will it take to save $20,000?
Starting from $2,000 and saving $500 a month at 4%, 2 years and 10 months (34 deposits). At $300 a month it takes 4 years and 6 months; at $1,000, 1 year and 6 months. The table below has more.
Does the interest rate make a big difference?
Over a year or two, not much: the deposits do almost all the work. Over 10 years it matters. To reach $100,000 in 10 years from zero you need $833 a month with no interest, $679 at 4% and $644 at 5%.
How big should an emergency fund be?
A common target is three to six months of essential spending – rent or mortgage, food, utilities, insurance, debt payments. Keep it in an account you can reach within days, not in investments that can fall in value when you need them.
Sources
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