Loan payment calculator
An amortising loan has a level payment that covers the interest and whatever principal is left over. The payment comes from one formula, applied here without rounding until the last step.
- Total repaid
- 24 045.54
- Total interest
- 4045.54
- Interest as a share of the loan
- 20.23 %
- Number of payments
- 60
- Interest in the first payment
- 125.00
- Principal in the first payment
- 275.76
Show the working
- Amount borrowed = 20 000
- Annual interest rate = 7.5
- Term = 5
- Payments per year = 12
- i = 7.5 / 100 / 12 = 0.006 25
- Number of payments = 5 * 12 = 60
- growth = (1 + 0.006 25)^60 = 1.453 29
- Payment = 0.006 25 == 0 ? 20 000 / 60 : 20 000 * 0.006 25 * 1.453 29 / (1.453 29 - 1) = 400.759
- Total repaid = 400.759 * 60 = 24 045.5
- Total interest = 24 045.5 - 20 000 = 4045.54
- Interest as a share of the loan = 4045.54 / 20 000 * 100 = 20.2277
- Interest in the first payment = 20 000 * 0.006 25 = 125
- Principal in the first payment = 400.759 - 125 = 275.759
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- i = annual rate / payments per year
- n = years x payments per year
- payment = P x i x (1+i)^n / ((1+i)^n - 1)
- When the rate is zero the payment is simply P / n.
The rate here is a nominal annual rate divided evenly, which is how almost every consumer loan quotes it. It is not the same as an effective annual rate.
The last payment in a real schedule differs by a few cents because lenders round each payment to the cent; this shows the unrounded level payment.
This is arithmetic, not financial advice. Real products carry fees, tax treatment and terms that no formula captures.
Frequently asked
Why is my total interest so high on a long loan?
Because interest is charged on the outstanding balance every period, and on a long term the balance stays high for years. Halving the term usually cuts total interest by far more than half.
What is the formula for a monthly loan payment?
payment = P i (1+i)^n / ((1+i)^n - 1), with i the monthly rate and n the number of months.