How compound interest grows your money
With simple interest, you earn the same amount every year, always on your first deposit. With compound interest, the interest is added to the balance and earns interest in turn. The difference is small at first and grows with time: that is the whole point of saving early. The calculator shows it with your own numbers. Type a starting amount, a yearly rate, a number of years and a monthly deposit, and read what the balance could be at the end.
Examples
- A lump sum. $10,000 at 5% a year for 10 years, with nothing added: $16,288.95 with yearly compounding, $16,470.09 with monthly compounding. The interest earned is $6,288.95 or $6,470.09.
- A lump sum and a monthly deposit. The same $10,000 at 5% for 10 years, plus $100 a month: $31,998.32 with monthly compounding. You put in $22,000; the other $9,998.32 is interest.
- Starting from zero. $200 a month at 5% with monthly compounding grows to $82,206.73 after 20 years ($48,000 paid in) and $166,451.73 after 30 years ($72,000 paid in). Ten more years of deposits add $24,000 of your money, and the interest grows by about $60,000.
These rates are examples to show how the calculation works, not a forecast. Nobody can promise a return: savings rates change, and investments can go down as well as up.
Monthly or yearly compounding
The two buttons in the bottom bar change how the yearly rate is turned into monthly growth.
- Monthly compounding divides the yearly rate by 12 and adds that interest every month. A 5% rate becomes 0.4167% a month, and over a year it grows money by a little more than 5% (about 5.12%).
- Yearly compounding uses the monthly rate that gives exactly the yearly rate after 12 months: (1 + rate) to the power 1/12, minus 1. Over a year, money grows by exactly 5%.
Which one should you pick? If your bank quotes an APY (in the US) or an AER (in the UK), that figure already includes compounding, so choose Yearly compounding. If you have a nominal rate that is credited monthly, choose Monthly compounding. In both cases, deposits are added at the end of each month.
The formula
Without deposits, the balance after n years with yearly compounding is A = P × (1 + r) to the power n. For $10,000 at 5% over 10 years: 10,000 × 1.05 to the power 10 = $16,288.95. With monthly deposits the calculator works month by month: each month, the balance earns its interest, then your deposit is added. The Year by year table shows the result at the end of every year: total paid in, interest so far and balance.
The rule of 72
To get a rough idea of how long money takes to double, divide 72 by the yearly rate. At 5%, about 14.4 years; at 6%, about 12. It is an approximation: at 6% with yearly compounding, $10,000 grows to $20,121.96 after 12 years, just over double. Use the calculator for the exact figure.
What the result does not include
The result is before tax and fees. Interest on savings may be taxed, depending on the account and where you live, and investment funds charge fees that reduce growth. Inflation also matters: a balance that grows 3% a year buys less if prices rise faster. Treat the figure as an estimate of how compounding works with your numbers, not as advice on where to put your money.
Related calculators
Borrowing is compounding in reverse: the loan calculator shows what a mortgage or car loan costs in interest. To see how much a few percentage points change things, compare two results with the percentage calculator. And if you are wondering how much you could put aside each month, start from your pay with the UK take-home pay calculator.
Your numbers are saved in your browser for your next visit. Currency, in the bottom bar, switches the symbol between $, £, €, C$ and A$, and Share gives a link that reopens the same calculation.