How your savings grow
Savings grow in two ways: from the money you put in and from the interest it earns. With compound interest, the interest is added to the balance and earns interest itself, so the longer you save, the faster the balance grows. This savings calculator takes your first deposit, what you plan to add every year or month, how fast those amounts rise, the interest rate and the tax on it, and shows the end balance and how much of it is interest.
The savings formula
- Initial deposit: P × (1 + r)n, where r is the yearly rate and n the number of years.
- Equal yearly deposits made at the end of each year: A × ((1 + r)n − 1) / r.
- Deposits that rise by g a year: A × ((1 + r)n − (1 + g)n) / (r − g); when g equals r, it is n × A × (1 + r)n − 1.
- Monthly deposits and other compounding: the calculator works month by month at the rate that matches the chosen compounding, (1 + r / k)k / 12 − 1, and takes the tax out of each month's interest.
Example
You deposit $20,000 and add $5,000 at the end of every year, 3% more each year, at 3% interest compounded annually. After 10 years you have $92,116.99: the $20,000 deposit, $57,319.40 of contributions and $14,797.59 of interest. With the formula: $20,000 × 1.0310 plus 10 × $5,000 × 1.039, because here the contributions rise as fast as the interest rate.
Contributions that grow
Most people save more as their income rises. The increase fields raise your contributions by a percentage every year: $5,000 a year with a 3% increase becomes $5,150.00 in the second year and $6,523.87 in year 10. Without the increase, the same plan ends at $84,197.72, $7,919 less.
How much monthly savings grow
Saving a fixed amount at the end of every month at 3%, starting from zero:
| Monthly deposit | 5 years | 10 years | 20 years |
|---|---|---|---|
| $100 | $6,458 | $13,945 | $32,685 |
| $250 | $16,145 | $34,862 | $81,714 |
| $500 | $32,290 | $69,724 | $163,427 |
| $1,000 | $64,581 | $139,448 | $326,854 |
How much to save each month for a goal
The monthly deposit that reaches each goal at 3%, starting from zero:
| Savings goal | In 5 years | In 10 years |
|---|---|---|
| $10,000 | $154.84 | $71.71 |
| $25,000 | $387.11 | $179.28 |
| $50,000 | $774.22 | $358.56 |
| $100,000 | $1,548.44 | $717.11 |
An emergency fund is a common first goal: three to six months of essential expenses in an account you can reach at any time. For a goal with a target date and a fixed return, the investment calculator finds the contribution directly.
Interest rate, compounding and tax
- Interest rate: savings accounts usually quote the APY, which already includes compounding; enter it and choose Annually.
- Compound: how often interest is added. The more often, the slightly more you earn; the result shows the equivalent annual rate. The compound interest calculator compares the frequencies.
- Tax: interest on savings is taxed as income. In the example, a 22% tax takes $3,169.77 and the balance ends at $88,557.68. Use 0 for tax-free accounts such as a Roth IRA.
- Inflation lowers what the money will buy; the interest calculator shows the balance in today's dollars.
Where to keep your savings
- High-yield savings and money market accounts: money you may need at any time, such as an emergency fund.
- Certificates of deposit: a fixed rate for a fixed time, usually higher than a savings account; see the CD calculator.
- Treasury bills: short-term government debt, free of state income tax.
- Investments: for goals many years away, such as retirement, where a higher but uneven return is worth the risk.
Deposits at banks insured by the FDIC, and at credit unions insured by the NCUA, are protected up to $250,000 per depositor, per institution and per ownership category.