How interest on savings is calculated
Interest is what a bank or an investment pays you for using your money. With compound interest, the interest is added to the balance and earns interest itself, so the balance grows faster every year. This interest calculator takes a starting amount, yearly and monthly contributions, the rate and how often it compounds, and shows the ending balance, how much of it is interest, the tax on it and what it is worth after inflation.
Interest formulas
- Compound interest: A = P × (1 + r / n)n × t, where P is the starting amount, r the yearly rate, n the number of compounding periods a year and t the years.
- Annual percentage yield (APY): (1 + r / n)n − 1; with continuous compounding, er − 1.
- Monthly rate used by the calculator: (1 + r / n)n / 12 − 1. Interest is credited every month at the rate that grows money exactly as much as the chosen compounding, so monthly contributions can be added on time.
- Tax: each month the interest × tax rate is taken out, so only the interest after tax keeps compounding.
- Buying power: ending balance / (1 + inflation rate)t.
Example
$20,000 invested at 5% compounded annually, with $5,000 added at the start of every year, grows to $54,535.20 in 5 years. You put in $45,000, so $9,535.20 is interest. With 3% inflation, the balance buys about as much as $47,042.54 today.
- Adding the $5,000 at the end of each year instead gives $53,153.79, $1,381 less, because each contribution earns a year less interest.
- Adding $416.67 at the start of every month gives $53,896.47: the same yearly amount, but most of it goes in later in the year.
Compounding frequency and APY
The more often interest compounds, the more you earn at the same rate. For a 5% rate, the annual percentage yield is:
| Compounding | APY |
|---|---|
| Annually | 5.000% |
| Semiannually | 5.062% |
| Quarterly | 5.095% |
| Monthly | 5.116% |
| Daily | 5.127% |
| Continuously | 5.127% |
Banks advertise savings accounts and CDs by their APY, so compare offers by APY, not by the stated rate. The calculator shows the equivalent annual rate under the results whenever interest compounds more than once a year.
How the balance grows over time
$20,000 at 5% compounded annually, with $5,000 added at the start of each year:
| Years | Money put in | Interest | Balance |
|---|---|---|---|
| 5 | $45,000 | $9,535 | $54,535 |
| 10 | $70,000 | $28,612 | $98,612 |
| 15 | $95,000 | $59,866 | $154,866 |
| 20 | $120,000 | $106,662 | $226,662 |
| 30 | $170,000 | $265,243 | $435,243 |
Over 30 years the interest is larger than everything you put in: this is compounding at work. At 5% money doubles in about 14.2 years; the rule of 72 gives a quick estimate, 72 / 5 = 14.4 years.
Simple vs. compound interest
Simple interest is paid only on the money you put in. $20,000 at 5% for 10 years earns $10,000 of simple interest but $12,578 with yearly compounding. Use the simple interest calculator for loans and bonds that pay simple interest, or the compound interest calculator to convert between compounding frequencies.
Tax and inflation
Interest from savings accounts, CDs and most bonds is taxed as ordinary income. In the example, a 22% tax on the interest takes $2,047.54 and leaves an ending balance of $52,259.47. Inflation then lowers what that money buys:
- a 5% rate taxed at 22% is a 3.90% return after tax;
- with 3% inflation, the real return is only about 0.87% a year: (1 + 3.90%) / (1 + 3%) − 1;
- if the rate after tax is lower than inflation, the savings lose buying power even though the balance grows;
- tax-advantaged accounts, such as a Roth IRA, let interest compound without that drag.
For savings with contributions that rise every year, use the savings calculator; for a single deposit held to maturity, the CD calculator.