Loan Payment Calculator

Payment = P × r ÷ (1 − (1 + r)^−n), where P is the amount borrowed, r the monthly interest rate and n the number of monthly payments. Within any month, interest = balance × r, and principal = payment − interest.

P

The amount borrowed, before any fees are added

r

The monthly interest rate: the annual rate divided by twelve

n

The number of monthly payments in the term

interest

The interest charged in a given month: the balance at the start of that month multiplied by r

principal

What is left of the payment once that month's interest is taken out — the only part that reduces what you owe

Use it when the payment is already known or already quoted and the question is what that payment is doing — most often in the first year of a long mortgage, where the gap between the payment and the progress it buys is at its widest. Read the interest column rather than the payment column: the payment is the same number in all twelve rows of the chart below, while the interest falls and the principal rises a little each month. Then compare two terms for the same amount and rate. A thirty-year term and a ten-year term put 39 percentage points between them in how much of the first year's payments is interest — 85.3% against 46.1% — and the only input that changed was the number of payments. If you are choosing between offers, this page is the one that shows the cost of the choice; if you need the full schedule rather than the first year, use the amortization calculator instead.

1. 250,000 at 6.5% over thirty years

   1. Monthly rate: 6.5 ÷ 12 = 0.5416667%, which is 0.005416667 as a decimal
   2. Payment: 250,000 × 0.005416667 ÷ (1 − 1.005416667^−360) = 1,580.17
   3. First payment: interest is 250,000 × 0.005416667 = 1,354.17, so principal is 1,580.17 − 1,354.17 = 226.00, and the balance falls to 249,774.00
   4. By the twelfth payment the interest has fallen to 1,340.33 and the principal risen to 239.84, leaving 247,205.69
   5. Year one in cash: 12 × 1,580.17 = 18,962.04, of which 16,167.73 is interest — 85.3% — and 2,794.31 is principal
   6. Over the whole term the interest is 318,861.58, so the loan costs 568,861.58 in total: 127.5% of the 250,000 borrowed

   The default case and the source of every figure in the chart below. The number worth pausing on is 2,794.31: that is a year of payments, and it is 1.1% of the loan. A thirty-year term is not thirty years of equal progress — the first year is almost entirely the cost of the money, and the principal only starts to move in the second half of the term.

2. The same 250,000 at 6.5% over ten years

   1. The monthly rate is unchanged at 0.005416667; only n falls from 360 to 120
   2. Payment: 250,000 × 0.005416667 ÷ (1 − 1.005416667^−120) = 2,838.70
   3. Year one in cash: 12 × 2,838.70 = 34,064.40
   4. Of that, 15,709.59 is interest (46.1%) and 18,354.81 is principal, leaving 231,645.19
   5. Total interest over the ten years: 90,643.89, against 318,861.58 over thirty

   Compare this with the row above rather than on its own. The payment is 80% higher, and in exchange the first year clears 18,354.81 of principal instead of 2,794.31 — 6.6 times as much — and the interest over the life of the loan falls by 228,217.69. The rate never changed. Everything that separates these two results comes from the term.

3. 100,000 at 12% over five years

   1. Monthly rate: 12 ÷ 12 = 1%, which is 0.01 as a decimal
   2. Payment: 100,000 × 0.01 ÷ (1 − 1.01^−60) = 2,224.44
   3. Year one in cash: 12 × 2,224.44 = 26,693.28
   4. Of that, 11,164.32 is interest (41.8%) and 15,528.96 is principal, leaving 84,471.04
   5. Total interest: 33,466.83, so the five-year loan costs 133,466.83 — a third of it interest

   A shorter loan at a higher rate. Even at twice the rate of the mortgage above, a five-year term keeps the first year's interest share down to 41.8%, because the balance is falling fast enough for each month's interest to be computed on a visibly smaller number. The rate sets how expensive the money is; the term sets how long you keep paying for it.

The payment is principal and interest only. Property taxes, homeowners insurance, mortgage insurance, association dues, origination fees and any other charge a lender collects alongside the payment are not in it, so the figure you owe each month will usually be larger than the one on this page — sometimes by a third. The rate is assumed fixed for the whole term: on an adjustable-rate loan the payment is recalculated whenever the rate resets, and the later years can look nothing like the first twelve rows here. Every payment is assumed to be made in full and on time, with no late charges, no missed months and no extra payments — a single extra payment applied to principal moves every row after it, and this page has no field for one. The chart stops at twelve months: it describes the first year, not the life of the loan, and if you need the whole schedule the amortization calculator is the page for that. The term is capped at 600 months, which is more than any consumer loan, and the rate at 50%. Amounts carry no currency symbol — they are right in whatever currency you typed them in, and meaningless in any other.

Why is almost all of my first year going on interest?

Because it is almost all going on interest. Interest is charged on the remaining balance, and at the start the remaining balance is the whole loan. On 250,000 at 6.5% the first payment is 1,580.17, and 1,354.17 of that is interest against 226.00 of principal. The proportion only starts to shift as the balance falls, which is why the same loan over ten years — 2,838.70 a month — gets 53.9% of its first year onto principal instead of 14.7%.

Does the monthly payment change during the loan?

On a fixed rate loan it does not, and that is exactly what makes the early years confusing: the payment column in the chart below is 1,580.17 in all twelve rows. What changes is the split inside that payment. Interest falls from 1,354.17 in month one to 1,340.33 in month twelve, and principal rises from 226.00 to 239.84 — a 6.1% increase across a single year, from a payment that never moved.

How much will I still owe after a year of payments?

On 250,000 at 6.5% over thirty years, 247,205.69. You will have handed over 18,962.04 and reduced the loan by 2,794.31, which is 1.1% of it. Enter your own amount, rate and term above to get your remaining balance, and remember that the figure assumes you make every payment in full and add nothing new to the loan.

How much difference does a shorter term make to the first year?

More than the payment difference suggests. On the same 250,000 at 6.5%, dropping from 360 months to 120 raises the payment from 1,580.17 to 2,838.70 — 80% more — while the principal cleared in year one goes from 2,794.31 to 18,354.81, which is 6.6 times as much. Over the whole loan the interest falls from 318,861.58 to 90,643.89.

What is an amortization schedule?

A table listing every payment in order and splitting each one into interest and principal, with the balance after it. The chart on this page is the first twelve rows of one, for the loan you entered. The full schedule for a thirty-year loan is 360 rows, which is why the amortization calculator exists as a separate page; the first year is enough to see the shape of it, because the shape barely changes after that.

• 12 CFR 1026.18 — Content of disclosures: the finance charge, the payment schedule and the total of payments that a lender must put in writing before you sign — Electronic Code of Federal Regulations, Office of the Federal Register (United States)
• 12 CFR 1026.7 — Periodic statement: where the split between interest and principal shows up once the loan is running, payment by payment — Electronic Code of Federal Regulations, Office of the Federal Register (United States)