How is the monthly instalment calculated?

With the annuity formula: principal × i ÷ (1 − (1 + i)^−n), where i is the yearly rate divided by twelve and n is the number of months. Every month the interest is charged on the balance still owed, so the principal part grows as the balance falls.

Does paying extra lower my instalment?

Not here. The extra amount goes straight to the principal while the instalment stays the same, so the loan finishes sooner and less interest is paid. Ask the lender to apply it to the principal rather than to the next instalment.

Why is the total interest higher than I expected?

Interest is charged on the balance, so on a long loan at a moderate rate the interest can approach, or with a large extra payment exceed, the amount borrowed. Shortening the term or paying extra reduces it, which the interest saved line reports.

Does this cover a loan with a fixed period then a floating rate?

No. It models one fixed rate for the whole term, and it leaves out arrangement fees, insurance and penalties. For a loan whose rate changes partway through, work out each period separately.

Loan Calculator

Loan calculator

A fixed-rate loan repaid in equal monthly instalments, with the schedule, the balance over time and the effect of paying a little extra. The arithmetic runs in the page.

Loan type Currency Amount borrowed Interest rate per year (%) Term (years) Extra payment per month

Monthly payment

—

Remaining balance over the life of the loan

Totals

Amount borrowed—

Total interest—

Total paid—

Instalments—

Final payment—

Paid off by—

Amounts are rounded to the nearest unit, so the last row of the schedule balances to within a unit.

Where the money goes

Across the whole loan

The first instalment

Year by year

Year	Opening balance	Principal paid	Interest paid	Closing balance

How the payment is worked out

The instalment is the annuity formula: P × i ÷ (1 − (1 + i)⁻ⁿ), where i is the yearly rate divided by twelve and n the number of months.
Every month the interest is charged on the balance that is still owed, so the principal part of the instalment grows over the term.
An extra payment is applied to the principal straight away, which shortens the term rather than lowering the instalment. That is how the interest saved and the time saved are worked out.
A rate of 0% is allowed and simply splits the amount across the months.
This models one fixed rate for the whole term. A loan with a fixed-rate period and a floating rate afterwards, or fees and insurance added on top, will differ.

About this tool

A loan is repaid in equal instalments, but the split inside each instalment changes every month: early on almost all of it is interest, and by the end almost all of it is principal. This works out the instalment with the annuity formula, builds the schedule behind it, and draws the balance as it falls. It also shows what happens when a little extra is paid each month, which shortens the term instead of lowering the instalment.

Questions

How is the monthly instalment calculated?: With the annuity formula: principal × i ÷ (1 − (1 + i)^−n), where i is the yearly rate divided by twelve and n is the number of months. Every month the interest is charged on the balance still owed, so the principal part grows as the balance falls.
Does paying extra lower my instalment?: Not here. The extra amount goes straight to the principal while the instalment stays the same, so the loan finishes sooner and less interest is paid. Ask the lender to apply it to the principal rather than to the next instalment.
Why is the total interest higher than I expected?: Interest is charged on the balance, so on a long loan at a moderate rate the interest can approach, or with a large extra payment exceed, the amount borrowed. Shortening the term or paying extra reduces it, which the interest saved line reports.
Does this cover a loan with a fixed period then a floating rate?: No. It models one fixed rate for the whole term, and it leaves out arrangement fees, insurance and penalties. For a loan whose rate changes partway through, work out each period separately.