Interest Calculator
With starting amount 10000 usd, annual rate 5 percent, years 10, interest comes to $16,470.09 — balance at the end. It is reached in 7 steps, the last of which is principal * pow(1 + rate / 100 / periods, periods * years), and each one is printed on the page with its numbers filled in. The formula is the one published by US SEC Investor.gov, not an approximation fitted to it.
What a balance grows to under simple and compound interest, with the gap between the two shown as its own figure.
By Alex Seote, Built and maintains Rule Calculator · Formula and sources checked · How we check
Starting amount 10000, Annual rate 5, Years 10, Compounded Monthly
$16,470.09
Balance at the end for the example below. Editing a field recomputes the calculator below; this figure holds the answer the page was loaded with.
It is written into the HTML rather than drawn by a script, so a search engine reading this page without running JavaScript still finds an answer.
- Simple interest
principal * rate / 100 * years$5,000- Balance, simple interest
principal + simple_interest$15,000- Balance, compound interest
principal * pow(1 + rate / 100 / periods, periods * years)$16,470- Compound interest
compound_total - principal$6,470- What compounding added
compound_total - simple_total$1,470- Effective annual rate
(pow(1 + rate / 100 / periods, periods) - 1) * 1005.116 %- Years to double at this rate
rate == 0 ? 0 : log(2) / (periods * log(1 + rate / 100 / periods))13.892
Worked example
$10,000 at 5% for ten years earns $5,000 of simple interest and $6,470.09 compounded monthly. The $1,470.09 between them is interest earned on interest — nothing was added and no better rate was found.
How to work it out yourself
- 1.Enter the starting balance, the annual rate and the number of years.
- 2.Choose how often interest is added. A savings account usually compounds daily and pays monthly; a bond pays simple interest twice a year and compounds nothing.
- 3.Compare the two totals. The gap is what compounding is worth, and it grows faster than the years do.
What the balance reaches over time
| Years | Balance at the end | Balance, simple interest | What compounding added |
|---|---|---|---|
| 1 | $10,511.62 | $10,500 | $12 |
| 2 | $11,049.41 | $11,000 | $49 |
| 3 | $11,614.72 | $11,500 | $115 |
| 5 | $12,833.59 | $12,500 | $334 |
| 7 | $14,180.36 | $13,500 | $680 |
| 10 | $16,470.09 | $15,000 | $1,470 |
| 15 | $21,137.04 | $17,500 | $3,637 |
| 20 | $27,126.40 | $20,000 | $7,126 |
| 25 | $34,812.90 | $22,500 | $12,313 |
| 30 | $44,677.44 | $25,000 | $19,677 |
| 40 | $73,584.17 | $30,000 | $43,584 |
On $10,000 at 5%, compounded monthly.
The formula
- Simple interest
principal * rate / 100 * years - Balance, simple interest
principal + simple_interest - Balance, compound interest
principal * pow(1 + rate / 100 / periods, periods * years) - Compound interest
compound_total - principal - What compounding added
compound_total - simple_total - Effective annual rate
(pow(1 + rate / 100 / periods, periods) - 1) * 100 - Years to double at this rate
rate == 0 ? 0 : log(2) / (periods * log(1 + rate / 100 / periods))
Source: US SEC Investor.gov — compound interest calculator and explanation
Questions people actually ask
- What is the difference between simple and compound interest?
- Simple interest is paid on the original amount only, for as long as the money is there. Compound interest is paid on the balance, so each payment joins the principal and earns in its turn. Over one year at the same rate the difference is small; over thirty it is most of the money.
- Does compounding more often make much difference?
- Less than people expect. On $10,000 at 5% for ten years, annual compounding gives $16,288.95 and daily gives $16,486.65 — under $200 across a decade. The rate matters enormously and the frequency barely does, which is why comparing accounts on the annual percentage yield rather than the compounding schedule is the right move.
- What is the effective annual rate?
- The single yearly rate that produces the same growth as the stated rate compounded through the year. 5% compounded monthly comes to 5.116% effective. It is the number to compare accounts on, and in the US a savings account has to advertise it as the APY.
- How long does money take to double?
- At 5% compounded monthly, about 13.9 years. The rule of 72 — divide 72 by the rate — gives 14.4, which is close enough for mental arithmetic between about 4% and 12% and drifts at the extremes. The exact figure is above and takes no rule at all.
- Is this what my savings account will pay?
- Only if the rate holds, and a variable rate rarely does. Bank rates move with the market, promotional rates expire, and tax is due on interest in most accounts. Treat the figure as arithmetic on a fixed rate rather than a forecast of what an account will actually deliver.
Related
- Compound Interest CalculatorFuture value of a starting balance plus monthly contributions, separating what you put in from what the interest earned.
- Savings Goal CalculatorThe monthly contribution needed to reach a target by a date, given what you have saved already.
- APY CalculatorAnnual percentage yield from a rate and its compounding frequency, and what it earns on a balance in dollars.
- ROI CalculatorReturn on investment as a total percentage and as an annualised rate, so holdings of different lengths compare fairly.
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