# Loan Repayment Calculator

> Work out the monthly instalment on a personal loan, what it costs in total, and what its APR actually is. A flat rate, an APR and a yearly rate charged monthly are three different things called the same word, so the tool asks which one you were quoted and converts between them. The month-by-month schedule downloads as a spreadsheet.

Use it: https://tessalor.com/en/money/loan-repayment

This tool runs entirely in the browser. Nothing entered into it is uploaded.

## Formula

```
A rate charged on what is still owed:

  i = r / 12                  a yearly rate, interest charged monthly
  i = (1 + r) ^ (1/12) - 1    an effective yearly rate (UK and EU APR)

  payment = P x i / (1 - (1 + i) ^ -n)

A flat rate, charged on the original amount for the whole term:

  interest = P x r x (n / 12)
  payment  = (P + interest) / n

The APR, recovered from the instalments by bisection. Find the monthly
rate j at which:

  advance = sum over k = 1..n of  payment(k) / (1 + j) ^ k

  APR, nominal    = j x 12
  APR, compounded = (1 + j) ^ 12 - 1

where
  r       = the advertised rate, as a decimal
  n       = the term, in months
  P       = the amount borrowed plus any fee added to the loan
  advance = the cash actually handed over, which excludes a financed fee
```

## Assumptions

- Every instalment is paid in full, one month apart, with the first one a month after the money arrives. A lender that takes the first payment on the day of drawdown is charging a slightly higher APR than this shows.
- The rate is fixed for the whole term. A variable rate is not modelled, and neither is a promotional rate that ends part way through.
- An arrangement fee is added to the loan rather than paid up front, so it is repaid with interest over the term. That is exactly why it raises the APR rather than leaving it alone.
- Interest is rounded to the cent every month, the way a lender's ledger does it, and the last instalment absorbs whatever the rounding left behind. It is normally within a few cents of the others.
- On a flat-rate loan the interest is fixed on the day the loan is drawn, and it is spread evenly across the instalments here. A lender using the Rule of 78 front-loads it instead, which changes neither the total nor the monthly payment and matters only if you settle early.
- Payment protection insurance, late fees and early settlement charges are not included. Every one of them makes the real cost higher than the figure shown.

## Inputs

| Name | Label | Type | Default | Range |
| --- | --- | --- | --- | --- |
| `amount` | Amount borrowed | currency | 12000 | 0 to 1000000 |
| `rate` | Advertised rate | percent | 7.9 | 0 to 100 |
| `rateBasis` | How the rate is quoted | select | monthly |  |
| `term` | Term | integer | 48 | 1 to 480 |
| `fee` | Arrangement fee | currency | 0 | 0 to 5000 |

## Outputs

- `monthlyPayment` — Monthly payment (currency), primary
- `totalRepaid` — Total you repay (currency)
- `costOfCredit` — Total cost of credit (currency)
- `aprEffective` — APR, compounded yearly (percent)
- `aprNominal` — APR, nominal yearly (percent)
- `finalPayment` — Final payment (currency)

## Questions

### Is a flat rate the same as an APR?

No, and the gap is large. A flat rate is charged on the original amount for the entire term, even though you are paying that amount down every month, so the same number costs roughly twice as much. On 12,000 over 48 months, 7.9% flat works out at 15.14% APR. Double a flat rate in your head before you compare it with anything.

### Why does 7.9% come out as an APR of 8.19%?

Because interest is charged twelve times a year, and interest charged in January is itself part of the balance in February. A yearly rate of 7.9% applied at 0.6583% a month compounds to 8.19% over the year. The United States quotes the 7.9% and calls it the APR; the United Kingdom and the European Union quote the 8.19%. Both figures are on the page so you can match whichever one your lender used.

### Is 0% finance really 0%?

Only if there is no fee. An arrangement fee is added to the loan and repaid with interest, so it is part of the cost of credit and part of the APR — which is precisely why the APR is a legally defined figure and the headline rate is not. Put the fee in and watch a 0% offer stop being 0%.

### Why is the last payment a different amount?

Because the instalment is rounded to the cent and 48 rounded instalments do not add up to the exact balance. Lenders resolve this the same way: the final payment clears whatever is left, usually within a few cents of the others. The tool shows it separately rather than hiding the difference in the total.

### Does a longer term cost more, even at the same rate?

Yes, and by more than most people expect. Interest is charged on what is still owed, so a longer term owes more for longer. At 9.9% on 10,000, the interest is 1,599.31 over 36 months and 3,901.46 over 84 — the same loan and the same rate, for two and a half times the interest.

### Is anything sent to a lender or stored anywhere?

No. The figures are worked out in this browser tab and there is no server to send them to. Nothing is saved, nothing is logged, and closing the tab is all it takes to get rid of them.

## Sources

- [Appendix J to Part 1026 — Annual Percentage Rate Computations for Closed-End Credit Transactions](https://www.consumerfinance.gov/rules-policy/regulations/1026/j/) — Consumer Financial Protection Bureau, applies to 2026. Retrieved 2026-07-30.
- [Directive 2008/48/EC on credit agreements for consumers, Annex I: the basic equation for the annual percentage rate of charge](https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX:32008L0048) — European Union (EUR-Lex), applies to 2026. Retrieved 2026-07-30.
- [The Consumer Credit (Total Charge for Credit) Regulations 2010 (SI 2010/1011)](https://www.legislation.gov.uk/uksi/2010/1011/contents/made) — The National Archives (legislation.gov.uk), applies to 2010. Retrieved 2026-07-30.

## Variants

- [Is a flat rate the same as an APR?](https://tessalor.com/en/money/loan-repayment/flat-rate-vs-apr)
- [What are the monthly repayments on a 10,000 loan?](https://tessalor.com/en/money/loan-repayment/on-a-10000-loan)

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Estimate, not advice. See https://tessalor.com/en/disclaimer.
Machine-readable catalogue: https://tessalor.com/api/tools.json