How the savings calculator works
A savings balance grows from two sources: the money you put in and the interest the bank pays on what is already there. Interest compounds, so each month's interest is calculated on the previous balance plus all the interest earned so far. The calculator simulates that month by month and reports the final balance, how much of it is your own deposits, and how much is interest, with a year-by-year table so you can see the curve bend.
The formula
Banks advertise APY, the yield after a full year of compounding, so the first step is to turn the APY into the monthly rate i that compounds to it. Then the balance after n months with a starting balance P and a deposit PMT at the end of each month is the future value of a lump sum plus the future value of an ordinary annuity:
i = (1 + APY)^(1/12) - 1 balance = P (1 + i)^n + PMT x ((1 + i)^n - 1) / i
Goal mode rearranges the same equation to find the deposit that lands exactly on a target:
PMT = (goal - P (1 + i)^n) x i / ((1 + i)^n - 1)
Worked example
The form defaults are a $1,000 starting balance, $200 deposited every month, 4% APY, and 10 years. The monthly rate is (1.04)^(1/12) - 1 = 0.32737%, and there are 120 months. Ten years of monthly compounding at that rate is exactly 1.04^10 = 1.480244:
balance = 1,000 x 1.480244 + 200 x (1.480244 - 1) / 0.00327374
= $1,480.24 + 200 x 146.6959
= $30,819.43Of that, $24,000 is your own money ($1,000 plus 120 deposits of $200) and $5,819.43 is interest. Year one ends at $3,483.69 with $83.69 of interest; by year ten the interest for the single year is $1,135.06, because the balance it is earned on has grown to $27,284. Flip the calculator to goal mode with a $50,000 target and the same inputs, and it reports a required deposit of $330.75 a month.
What $200 a month grows to
Starting from zero, at three realistic savings-account yields. The deposits total $12,000, $24,000, and $48,000 for the three columns; everything above that is interest.
| APY | 5 years | 10 years | 20 years |
|---|---|---|---|
| 3% | $12,916 | $27,890 | $65,371 |
| 4% | $13,236 | $29,339 | $72,768 |
| 5% | $13,563 | $30,873 | $81,161 |
Monthly deposit needed for a goal at 4% APY
Starting from zero. Notice that doubling the time cuts the deposit by more than half, because the early deposits earn interest for longer.
| Goal | In 3 years | In 5 years | In 10 years |
|---|---|---|---|
| $10,000 | $262.18 | $151.11 | $68.17 |
| $25,000 | $655.46 | $377.76 | $170.42 |
| $50,000 | $1,310.92 | $755.53 | $340.84 |
| $100,000 | $2,621.84 | $1,511.05 | $681.68 |
APY versus the monthly rate
If a bank paid 4% divided into twelve equal monthly instalments of 0.3333%, compounding would push the yearly growth to 4.074%, and the bank would have to advertise that as its APY. Advertising 4% APY means the true monthly rate is a touch lower, 0.3274%, so that twelve compounded months come to exactly 4%. The difference is small (about $7 a year on $10,000), but the calculator uses the exact conversion so its yearly figures match your statements.
Tips for using the calculator
- Emergency fund: put your monthly expenses times three to six in goal mode and see what it takes to get there in a year or two.
- Windfalls: a bonus or tax refund goes in the starting balance; the calculator shows how much of the final total it becomes.
- Rate shopping: re-run with 0.5% APY and 4.5% APY to see what a high-yield account is worth over your horizon.
- Ranges: type
3~5in the APY box to see a band of outcomes instead of a single number.