Interest capitalization calculator
Rolling 500 of unpaid interest into a 10,000 loan makes the balance 10,500, and at 6% over 60 months the payment rises from 193.33 to 202.99. See what a grace period or a paused loan really costs. Free in your browser.
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Worked example
- Principal amount
- 10,000
- Unpaid interest
- 500
- New principal balance
- 10,500
- Monthly payment before capitalization
- 193.33
- Monthly payment after capitalization
- 202.99
- Monthly payment change
- 9.67
free
What happens when interest is capitalized
Capitalization folds interest that has built up but not been paid back into the loan balance. It often happens after a pause in payments, such as the grace period of a student loan or a forbearance or deferment. The new balance is simply the old principal plus the unpaid interest: 10,000 carrying 500 of deferred interest becomes 10,500. From that point the added amount is treated as principal, so future interest is charged on it too.
Seeing the effect on your payment
If you also enter the annual rate and the number of months, the calculator works out a fixed monthly payment for the balance before and after capitalization, using a monthly rate of one twelfth of the annual rate. At 6% over 60 months, 10,000 costs 193.33 a month and 10,500 costs 202.99, a difference of 9.67. The rate and the term go together; leave both out and you get the new balance alone. If the rate is zero, the payment is the balance divided by the months, so you still get a sensible figure.
What you can do with it
Deferment payoff
Capitalize skipped interest after a forbearance and quote the borrower's higher re-amortized payment.
Student loans
Show how unpaid interest during a grace period raises the balance before repayment begins.
FAQ
How is rounding handled?
Half-up to the decimals places (default 2), with each field rounded once from the raw value rather than from another rounded field.
What does it mean when interest is capitalized?
Interest that built up but was not paid is added to the loan balance. From then on it is part of the principal, so 10,000 with 500 of unpaid interest becomes a balance of 10,500.
Why does my payment go up after capitalization?
Because the payment is now worked out on a bigger balance, and the added interest starts earning interest itself. The calculator re-amortizes both balances at the same rate and term, so the difference shows what capitalization costs each month.
Do I have to enter a rate and a term?
No. They are optional and go together: with both you also get the payments before and after, and without them you get the new balance only. The term must be a whole number of months.
When does interest get capitalized?
Usually after a period when payments were paused, such as the grace period of a student loan or a forbearance or deferment. The unpaid interest is rolled into the balance before regular repayment starts again.
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/finance/interest-capitalization \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"principal":10000,"unpaid_interest":500}'const res = await fetch("https://api.kit.forhosting.com/finance/interest-capitalization", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"principal": 10000,
"unpaid_interest": 500
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/finance/interest-capitalization",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"principal": 10000,
"unpaid_interest": 500
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/finance/interest-capitalization", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"principal":10000,"unpaid_interest":500}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"principal":10000,"unpaid_interest":500}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/finance/interest-capitalization", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"principal": 10000,
"unpaid_interest": 500
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "finance.interest_capitalization",
"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
Adds unpaid_interest to principal to get the new capitalized balance, then—if you supply annual_rate and months—re-amortizes both to show payment_before, payment_after and the payment_delta.
The capitalization math
When the periodic rate rounds to essentially zero the formula degrades gracefully to principal divided by months, avoiding a division-by-zero blow-up and still returning a sensible installment. Capitalization folds accrued but unpaid interest back into the loan balance: new_principal equals principal plus unpaid_interest, so a $10,000 balance carrying $500 of deferred interest becomes $10,500. When you also pass annual_rate and months, the tool re-amortizes both the old and the new balance with the standard fixed-payment formula, payment = P·i·(1+i)^n / ((1+i)^n − 1), where i is annual_rate divided by 100 and then by 12, and n is months. At 6% over 60 months the $10,000 balance costs $193.33 a month while the $10,500 balance costs $202.99, so payment_delta is $9.67.
Inputs, rounding and validation
principal must be a finite number strictly greater than zero and unpaid_interest a finite number of zero or more; violating either returns a typed invalid_input error that names the offending field instead of an untyped throw. annual_rate and months are optional and travel together: months must be a positive integer and annual_rate zero or more, otherwise the payment block is simply omitted and you receive only principal, unpaid_interest and new_principal.
When to reach for it
Use this whenever a lender rolls a forbearance, deferment or negative-amortization shortfall into the balance and you need to quote the borrower's new installment. Omit annual_rate and months when you only want the capitalized balance—for example, showing that skipping interest during a grace period lifts a student loan from $10,000 to $10,500 before any re-amortization happens. Failed tasks are never charged, and prepaid balance is spent only on successful API calls at the published base rate.
Integration use cases
Loan servicing
Batch new_principal and payment_delta across a whole portfolio through the JSON API.
Technical questions
What does capitalization do?
It adds unpaid_interest to principal, so new_principal = principal + unpaid_interest, then optionally re-amortizes the payment.
How is the payment calculated?
With the fixed-rate annuity formula using annual_rate/12 as the monthly rate over months; a near-zero rate falls back to principal/months.
Are annual_rate and months required?
No. Omit them and you get just the capitalized balance; supply both to also get payment_before, payment_after and payment_delta.
Is it free?
Yes in the tier A browser widget; the deterministic API starts at $0.002 and only successful calls are billed.