Loan Payment Calculator: the PMT Formula

Written byOleh Soloninupdated 25 September 2026

Currency

Loan amount

PV (present value): current principal amount.

Annual interest rate, %

Annual nominal rate. Rate per period = annual rate / 12.

Term (months)

Total number of periods (months).

Result

Monthly payment

$705.12

Total paid

$16,922.92

Total interest

$1,922.92

Interest in the first payment

$148.25

Working, step by step

1. Monthly rate: r = 11.86 ÷ 12 ÷ 100 = 0.009883 2. (1 + r)^n = 1.009883^24 = 1.266219 3. Factor: r × (1 + r)^n ÷ ((1 + r)^n − 1) = 0.04700812 4. Payment: 15,000 × 0.04700812 = 705.12

Spreadsheet formula

=PMT(11.86%/12, 24, -15000)

This result is informational only and is not professional advice.

Principal$15,000.00

Interest$1,922.92

Balance trend

Month 1$14,443.13

Month 5$12,160.06

Month 9$9,785.38

Month 13$7,315.43

Month 17$4,746.37

Month 21$2,074.23

Payment schedule

Period	Payment	Interest	Principal	Balance
1	$705.12	$148.25	$556.87	$14,443.13
2	$705.12	$142.75	$562.38	$13,880.75
3	$705.12	$137.19	$567.93	$13,312.82
4	$705.12	$131.58	$573.55	$12,739.27
5	$705.12	$125.91	$579.22	$12,160.06
6	$705.12	$120.18	$584.94	$11,575.12
7	$705.12	$114.40	$590.72	$10,984.40
8	$705.12	$108.56	$596.56	$10,387.84
9	$705.12	$102.67	$602.46	$9,785.38
10	$705.12	$96.71	$608.41	$9,176.97
11	$705.12	$90.70	$614.42	$8,562.55
12	$705.12	$84.63	$620.50	$7,942.05
13	$705.12	$78.49	$626.63	$7,315.43
14	$705.12	$72.30	$632.82	$6,682.60
15	$705.12	$66.05	$639.08	$6,043.53
16	$705.12	$59.73	$645.39	$5,398.14
17	$705.12	$53.35	$651.77	$4,746.37
18	$705.12	$46.91	$658.21	$4,088.16
19	$705.12	$40.40	$664.72	$3,423.44
20	$705.12	$33.83	$671.29	$2,752.15
21	$705.12	$27.20	$677.92	$2,074.23
22	$705.12	$20.50	$684.62	$1,389.61
23	$705.12	$13.73	$691.39	$698.22
24	$705.12	$6.90	$698.22	$0.00

The loan payment formula with your numbers, one step at a time

Work out a fixed loan payment with the PMT formula, step by step: the monthly rate, the payment factor and the payment with your numbers, plus total interest, the first month's interest and the spreadsheet formula.

A fixed loan payment is the same amount every month until the loan is repaid. Inside it, the split changes: the interest share falls and the principal share grows, though interest does not always make up most of the early payments. The payment comes from a single formula, and this page shows it with your own numbers, step by step.

Alongside the payment you get the total interest, the interest in the first payment and a PMT formula you can paste into a spreadsheet to get the same figure. For a full schedule with extra repayments, use the loan calculator.

How to use

Enter the loan amount, the annual interest rate and the term in months.
Read the monthly payment, total interest and the interest in the first payment.
Follow the working: monthly rate, power, payment factor and payment.
Copy the spreadsheet formula to compare options in a sheet.

The loan payment formula

Payment = P × r × (1 + r)^n ÷ ((1 + r)^n − 1), where P is the loan amount, r the monthly rate as a decimal (annual rate ÷ 12 ÷ 100) and n the number of months. Written another way: P × r ÷ (1 − (1 + r)^−n).

The part r × (1 + r)^n ÷ ((1 + r)^n − 1) is the payment factor: the payment is the loan amount multiplied by it. It depends only on the rate and the term.

A worked example by hand

A 15,000 loan at 11.86% over 24 months. 1) Monthly rate: 11.86 ÷ 12 ÷ 100 = 0.009883. 2) (1 + r)^n = 1.009883^24 = 1.266219. 3) Factor: 0.04700812. 4) Payment: 15,000 × 0.04700812 = 705.12.

Over 24 months you repay 16,922.92, of which 1,922.92 is interest. The first payment is 148.25 interest and 556.87 principal, and after a year the balance is 7,942.05.

Payment factor and payment on 10,000

A longer term lowers the factor but raises the interest: over ten years a 10,000 loan at 11.86% costs 7,119.54 in interest.

Rate 11.86% a year. Worked out with this calculator.
Term	Factor	Payment on 10,000	Total interest
12 months	0.08878331	887.83	654.00
24 months	0.04700812	470.08	1,281.95
36 months	0.03314748	331.47	1,933.09
60 months	0.02217377	221.74	3,304.26
120 months	0.01426628	142.66	7,119.54

PMT in a spreadsheet

Spreadsheets have the same formula built in: =PMT(rate/12, number of months, -loan amount). For the example, =PMT(11.86%/12, 24, -15000) returns 705.12. The loan amount goes in as a negative so that the payment comes out positive, because money received and money paid flow in opposite directions.

Fixed payments or declining payments

With declining payments the principal is repaid in equal parts and interest is charged on what is left, so each payment is smaller than the last. Fixed payments are easier to budget, but cost more interest because the balance falls more slowly at first.

Worked out from this calculator's schedule.
15,000 at 11.86% over 24 months	Fixed	Declining
First payment	705.12	773.25
Last payment	705.12	631.18
Balance after a year	7,942.05	7,500.00
Total interest	1,922.92	1,853.13

What this calculator shows

The monthly payment and total repaid
Total interest and the interest in the first payment
The formula worked through with your numbers
A PMT spreadsheet formula with the same inputs

What to keep in mind

The rate is fixed and payments are monthly and equal, with interest at the annual rate ÷ 12.
Lenders may accrue interest by the day, so the interest in their schedule can differ noticeably from month to month — less in February, more in 31-day months.
Fees and insurance are not part of the formula.

Where the numbers come from

Checked against the standard annuity payment formula.

FAQs

What is the formula for a loan payment?

Payment = P × r × (1 + r)^n ÷ ((1 + r)^n − 1), with P the loan, r the monthly rate as a decimal and n the months. A 15,000 loan at 11.86% over 24 months gives 705.12.

How do I calculate a loan payment by hand?

Divide the annual rate by 12 and by 100, raise (1 + r) to the number of months, work out the factor r × (1 + r)^n ÷ ((1 + r)^n − 1) and multiply it by the loan. The calculator shows each step with your numbers.

How do I use PMT in a spreadsheet?

=PMT(rate/12, months, -loan). For example =PMT(11.86%/12, 24, -15000) gives 705.12. The minus sign makes the payment positive.

What is a payment factor?

The share of the loan amount that one monthly payment makes up. At 11.86% over 24 months it is 0.04700812, so each 10,000 borrowed costs 470.08 a month.

Why is so much of the first payment interest?

Interest is charged on the balance, which is largest at the start. On 15,000 at 11.86% the first payment is 148.25 interest and 556.87 principal.

How do I find the total interest?

Multiply the payment by the number of months and subtract the loan: 705.12 × 24 − 15,000 is about 1,922.88; the exact schedule total is 1,922.92.

Why does my lender quote a different payment?

Lenders may accrue interest daily, round the payment and add fees or insurance to the loan. The formula here is the base calculation without those.

Worked example

Payment on a 15,000 loan

Input: Loan 15,000; rate 11.86%; 24 months

Output: Payment 705.12; total interest 1,922.92

Note: Payment factor 0.04700812. In a spreadsheet: =PMT(11.86%/12, 24, -15000).

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Loan Payment Calculator: the PMT Formula

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