Rule of 78 rebate calculator
Settle a 48-month loan after 18 payments with 3000 of total interest and the Rule of 78 gives you back 1186.22, while the lender keeps 1813.78. You also see how many periods were left. Free in your browser.
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- Runs in your browser
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- Your data stays on your device
Run — free
Worked example
- Total loan periods
- 48
- Periods paid
- 18
- Total finance charge
- 3,000
- Periods remaining
- 30
- Unearned-interest rebate
- 1,186.22
- Earned interest
- 1,813.78
free
What the Rule of 78 rebate is
Some installment loans fix the whole finance charge at the start and use the Rule of 78, or sum-of-the-digits method, to decide how much of it each month earns. Early months earn the most. If you settle the loan before the end, the lender owes you a rebate of the interest not yet earned. This calculator takes three numbers, the original number of installments, the installments already paid and the total interest, and returns the rebate, the interest the lender keeps and the periods still remaining. For a 48-month loan with 18 payments made and 3000 of total interest, 30 periods remain, the rebate is 1186.22 and the lender keeps 1813.78.
Reading the result correctly
The most common mistake is to expect a proportional refund. Paying off a 12-month loan at month 6 returns about 26.9% of the interest, not half, because the rule front-loads the charge. The method is a fixed weighting rather than a new amortization, so the same inputs always give the same rebate, which makes it useful for checking payoff statements and early-termination refunds. Amounts are plain numbers with no currency, rounded to two decimals by default; apply your own currency and any legal rounding on top.
Reading and auditing the result
Because the method is a fixed algebraic weighting rather than a re-amortisation, identical inputs always return an identical rebate, which suits auditing payoff statements, reconciling early-termination refunds, or teaching why the Rule of 78 favours the lender against the actuarial simple-interest method on long terms. A 12-month loan paid to month 6 refunds (6 × 7)/(12 × 13) ≈ 26.9% of interest, not 50% — exactly the front-loading the rule encodes.
Values are plain numbers with no currency assumed, so callers apply their own currency and any regulatory rounding on top.
What you can do with it
Early-payoff refund audit
Verify the unearned-interest rebate a lender must return when a borrower clears an instalment loan ahead of schedule.
Finance teaching
Show how sum-of-the-digits weighting front-loads interest and why a mid-term payoff refunds far less than half of the finance charge.
FAQ
What do the outputs mean?
Both amounts round half-up to decimals (default 2).
How much interest do I get back if I pay off a 12-month loan halfway?
About 26.9% of the total interest, not 50%. Paying to month 6 leaves 6 periods, and the rebate is 6 × 7 divided by 12 × 13, because the rule loads most of the interest into the early months.
How is the Rule of 78 rebate calculated?
Take the installments still remaining, multiply that count by itself plus one, and divide by the original term times itself plus one. The total interest times that fraction is your rebate; the rest is interest the lender has earned.
Why is the Rule of 78 worse for the borrower than simple interest?
Because it front-loads the finance charge, so early installments count as mostly interest. On long terms, a borrower who settles early gets back less than under the actuarial simple-interest method, which is why the rule favours the lender.
Why is it called the Rule of 78?
Because the digits 1 through 12 of a one-year loan add up to 78. The same triangular weighting works for any term, using the number of installments times that number plus one.
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/rule-of-78-rebate \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"n":48,"k_paid":18,"total_interest":3000}'const res = await fetch("https://api.kit.forhosting.com/finance/rule-of-78-rebate", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"n": 48,
"k_paid": 18,
"total_interest": 3000
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/finance/rule-of-78-rebate",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"n": 48,
"k_paid": 18,
"total_interest": 3000
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/finance/rule-of-78-rebate", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"n":48,"k_paid":18,"total_interest":3000}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"n":48,"k_paid":18,"total_interest":3000}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/finance/rule-of-78-rebate", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"n": 48,
"k_paid": 18,
"total_interest": 3000
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "finance.rule_of_78_rebate",
"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
Computes the Rule of 78 unearned-interest rebate from three inputs — the original term n, the instalments already paid k_paid and the total_interest of the loan — returning the rebate owed to the borrower, the interest earned by the lender and the periods still remaining. API from $0.002.
The sum-of-the-digits rebate formula
The Rule of 78, or sum-of-the-digits method, front-loads a loan's finance charge, so a borrower who settles early is owed a rebate of the interest not yet earned. This capability computes that rebate with the closed-form ratio rebate = total_interest × (u × (u + 1)) / (n × (n + 1)), where n is the original number of instalments and u = n − k_paid is the count of periods still remaining. For a 48-month loan with 18 payments made and 3000 of total_interest, u is 30, so the rebate is 3000 × (30 × 31) / (48 × 49) = 1186.22 and the interest_earned by the lender is total_interest − rebate = 1813.78. The name comes from the digits 1 through 12 of a one-year loan summing to 78; that triangular weighting generalises to any term through the n(n + 1) denominator returned in periods_remaining.
Inputs, validation and rounding
The optional decimals field defaults to 2. Three fields are required and each is range-checked before any arithmetic runs. n, the total instalment count, must be an integer of at least 1; k_paid, the instalments already paid, must be an integer between 0 and n inclusive; and total_interest must be a number that is zero or positive. Anything else returns a typed invalid_input error naming the offending field, such as 'k_paid inválido', so a form can highlight it and no task is charged. Both money outputs, rebate and interest_earned, are rounded once with an explicit half-up rule applied to the raw IEEE value — never chained off an already-rounded figure — and they always sum back to total_interest. periods_remaining is returned as the exact integer u, with no rounding, so the caller can re-derive the ratio independently.
Reading and auditing the result
The rebate is largest when few payments have been made and shrinks quadratically as k_paid approaches n, because u(u + 1) falls with the square of the periods remaining. Two edge cases are worth checking: k_paid = n yields periods_remaining 0 and a zero rebate, while k_paid = 0 returns the entire finance charge.
Integration use cases
Loan servicing automation
Batch the same n / k_paid / total_interest contract through the API to recompute rebates across a whole portfolio of accounts.
Technical questions
What formula does this use?
The sum-of-the-digits Rule of 78: rebate = total_interest × u(u+1) / (n(n+1)), where u = n − k_paid is the number of periods remaining.
What happens if k_paid equals n or 0?
k_paid = n gives periods_remaining 0 and a zero rebate; k_paid = 0 returns the entire total_interest as the rebate.
How are invalid values handled?
A non-integer or out-of-range n or k_paid, or a negative total_interest, returns a typed invalid_input error naming the field. Failed tasks are never charged.
Is it free?
The tier-A widget runs free in your browser; the deterministic API contract is billed from $0.002 on successful tasks only.