Compound growth calculator
Grow 1,000 at 5% per period for 10 periods and it reaches 1,628.89462678, because each period's gain starts earning too. Enter a starting amount, a fixed rate and a horizon to project savings, users or revenue. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Amount
- 1,000
- Interest rate
- 5
- Periods
- 10
- Growth factor
- 1.62889463
- Future value
- 1,628.89462678
- Growth
- 628.89462678
Compound growth is what happens when a fixed rate is applied not only to the starting amount but also to every increment already earned. A savings balance, a user base, a revenue line, or a classroom homework figure all follow the same identity: the future value equals the initial value times one plus the periodic rate, raised to the number of periods.
What compound growth means and how the future value appears
Compound growth is the discrete counterpart of exponential growth: each period the quantity is multiplied by the same factor, so earlier growth itself starts earning growth. If the initial value is amount and the periodic rate as a percent is rate, the multiplier for one period is one plus rate divided by one hundred. After periods steps that multiplier has been applied that many times, which is exactly (1 + rate/100) raised to periods, and the future value is amount times that factor.
When the rate is zero the factor is one and the amount is unchanged. When the number of periods is zero the same identity returns the original amount, which is the honest answer for a horizon that has not started. A negative rate models a constant contraction: the quantity shrinks each period, and the future value lands below the initial value as long as the rate stays above negative one hundred percent so that the factor stays positive.
What you can do with it
Savings and investment projections
Turn a starting balance, a fixed periodic return, and a horizon into the future value and the absolute increment for articles, planners, and landing-page widgets.
Users, revenue, and other operating metrics
Project a user base, seat count, or recurring-revenue line at a constant period-over-period rate without opening a spreadsheet for each scenario.
Classroom time-value checks
Let students submit amount, rate, and periods and verify the compounded final value, including the hard fail when the period count is negative.
FAQ
How is the future value of compound growth calculated?
Multiply the initial amount by (1 + rate/100) raised to the number of periods.
What happens if the number of periods is negative?
A negative horizon is not accepted; enter zero or more compounding periods. Failed validation is not billed.
Is the rate a percent or a decimal fraction?
Enter rate as percent points per period, not as a decimal fraction — five means five percent per period, not 0.05. The engine divides by one hundred before raising the factor.
Can the rate be negative, and what does zero periods return?
A negative rate models contraction and shrinks the future value, as long as the rate is greater than −100% so that 1 + rate/100 stays positive. Zero periods returns the original amount unchanged.
Does it account for regular deposits along the way?
No. It projects a single starting amount at one fixed rate over one horizon. If you add money every period, combine this result with your own contribution schedule.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/fin/compound-growth \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"amount":1000,"rate":5,"periods":10}'const res = await fetch("https://api.kit.forhosting.com/fin/compound-growth", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"amount": 1000,
"rate": 5,
"periods": 10
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/fin/compound-growth",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"amount": 1000,
"rate": 5,
"periods": 10
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/fin/compound-growth", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"amount":1000,"rate":5,"periods":10}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"amount":1000,"rate":5,"periods":10}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/fin/compound-growth", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"amount": 1000,
"rate": 5,
"periods": 10
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "fin.compound_growth",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
This compound growth calculator takes those three inputs, returns the final value together with the growth factor and the absolute increment, and fails with invalid_input when the period count is negative instead of inventing a reverse-time story.
What compound growth means and how the future value appears
A worked example: one thousand growing at five percent per period for ten periods has growth_factor 1.62889463 and future_value 1628.89462678 after half-up rounding to eight decimals, so the absolute growth is 628.89462678.
Input contract, response shape, and error behaviour
Pair the result with your own contribution schedule if you need deposits along the way; start here when the product question is a transparent, three-input future value for a page, a worksheet, or a batch of scenarios that already share one rate and one horizon. POST a JSON body with three required finite numbers: amount (the initial value that will grow, any finite number including zero; aliases initial, principal, present_value, pv, value), rate (the fixed growth rate per period as a percent such as five for five percent; aliases growth_rate, rate_percent, percent), and periods (the compounding count, greater than or equal to zero; aliases n, steps, horizon). Each field may arrive as a JSON number or as a numeric string. Missing fields, empty strings, booleans, and non-finite values fail with invalid_input naming the field and are not billed. If rate is less than or equal to negative one hundred percent, one plus r is not positive and the power is not a useful real factor, so that case is invalid_input as well. On success the body echoes amount, rate and periods; reports growth_factor rounded half-up to eight decimals; returns future_value and growth rounded the same way; and includes a short formula string restating the identity future_value equals amount times (1 + rate/100) to the power periods.
Where a compound growth calculator earns its keep
Educators teaching the difference between simple interest and compound growth can seed classroom examples that show one thousand at five percent for ten periods versus the linear alternative, and can demonstrate the hard fail when someone types a negative period count. Failed validation does not consume balance. Product and finance teams projecting users, seats, or recurring revenue at a constant period-over-period rate can post the same three numbers the model already stores and quote a stable future_value with an eight-decimal contract. Because the implementation is tier A parse, every successful call costs the published $0.002 base price with no model tokens and no outbound network. Keep the rate above negative one hundred percent, keep periods at zero or more, pin the rounded future_value in tests, and you get reproducible compound-growth results for widgets, CMS embeds, and edge workers without standing up a spreadsheet service of your own.
Technical questions
What does the compound growth calculator cost?
The browser tool is free. API requests use prepaid balance at $0.002 per successful call; invalid input is not billed.