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Mortgage payments explained: how the monthly math actually works

The amortization formula in plain English. Why your first payment is almost all interest, how a 30-year vs 15-year mortgage really compares, and what changes when rates move 1%.

ToolHub TeamJune 8, 202612 min read

A mortgage payment is one of the largest recurring bills most people ever sign up for, and yet the math behind it is often treated as a black box: type your numbers into a calculator, get a payment. This guide takes the lid off. By the end you will be able to recreate the calculation in a spreadsheet, see why your first payment is mostly interest, understand why a 1% rate change costs so much, and know exactly what your amortization schedule does month by month.

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Monthly payment, total interest, and full amortization schedule

The formula

The standard monthly payment formula for a fixed-rate mortgage is:

M = P × r × (1 + r)ⁿ / ((1 + r)ⁿ − 1)

Where:

  • M = monthly payment
  • P = principal (loan amount)
  • r = monthly interest rate (annual rate divided by 12)
  • n = total number of monthly payments (years × 12)

It looks intimidating but it is just compound interest rearranged. The mortgage is structured so each payment is the same dollar amount; the formula solves for that constant.

Worked example: $400,000 at 7% for 30 years

Most common US mortgage scenario as of mid-2026. Let us plug it in:

  • P = 400,000
  • r = 0.07 / 12 = 0.005833 (monthly rate)
  • n = 30 × 12 = 360 (months)

Calculate the (1 + r)ⁿ part first: 1.005833^360 ≈ 8.116. Then:

  • Numerator: 400,000 × 0.005833 × 8.116 = 18,936
  • Denominator: 8.116 − 1 = 7.116
  • Monthly payment M = 18,936 / 7.116 = $2,661

Over 30 years (360 payments), the total paid is 2,661 × 360 = $958,012. Of that, $400,000 is the original loan, and $558,012 is interest. You pay 1.4x the home price just in interest over a 30-year mortgage at 7%.

Why the first payment is almost all interest

Each month, the bank charges interest on the remaining balance at the monthly rate. In month 1, the full $400,000 is outstanding, so:

Month 1 interest = 400,000 × 0.005833 = $2,333

Your payment is $2,661. The interest takes $2,333, and only $328 goes to paying down principal. The remaining balance after month 1 is $400,000 − $328 = $399,672.

In month 2, interest is charged on $399,672 (a tiny bit less), so a tiny bit more goes to principal. By month 60 (year 5), you are still putting more toward interest than principal. The crossover happens around year 20 of a 30-year loan at 7%.

The amortization schedule

Here is what the first 5 years look like on our $400K example:

Interest / PrincipalRemaining balance
Month 1$2,333 / $328$399,672
Month 12$2,322 / $339$396,090
Month 24$2,297 / $364$389,810
Month 36$2,270 / $391$383,074
Month 48$2,242 / $419$375,856
Month 60$2,210 / $451$368,123

Notice: after 5 years (60 payments of $2,661 = $159,660 paid), you have only reduced the loan by $32,000. The other $128,000 went to interest. This is why early mortgage years feel like you are not making progress.

How much does a 1% rate change cost?

Comparing the same $400K, 30-year loan at different rates:

Monthly paymentTotal interest paid
5% rate$2,147$373,023
6% rate$2,398$463,353
7% rate$2,661$558,012
8% rate$2,935$656,533
9% rate$3,218$758,422

Each 1% increase adds roughly $250-280 per month and $90-100K total interest on a $400K loan. This is why people refinance when rates drop even 1% — it can save tens of thousands of dollars over the loan's life.

15-year vs 30-year mortgages

Same $400K loan, same 7% rate, different terms:

Monthly paymentTotal interest paid
30-year term$2,661$558,012
20-year term$3,101$344,256
15-year term$3,595$247,153
10-year term$4,644$157,237

A 15-year mortgage costs $934 more per month but saves $310,859 in interest. The shorter term is cheaper because each payment makes a much bigger dent in principal — the loan compounds for less time.

The flip side: that $934 per month is real, and many people cannot afford the 15-year payment. The 30-year is more popular because it makes a larger house affordable today, with the trade-off of more total interest.

What else is in your payment (PITI)

The mortgage payment formula gives you principal and interest (P + I). The check you actually send each month usually includes two more items:

Property taxes (T)

Annual taxes typically range from 0.5% to 2.5% of home value, depending on the state. The lender escrows 1/12 of the annual bill into your payment. On a $500K home in a 1.5% tax state, that is $625/month added to your mortgage.

Insurance (I)

Homeowners insurance runs $1,000 to $3,000+ per year depending on coverage and region. Also escrowed monthly. Add another $100-250/month.

PMI (Private Mortgage Insurance)

Required by most lenders if your down payment is under 20%. Costs 0.3% to 1.5% of the loan amount per year. On a $400K loan: $100 to $500 per month. PMI drops off automatically when your loan-to-value ratio reaches 78%.

The full PITI on our example

$500K home, 20% down ($100K), $400K loan at 7% for 30 years, in a 1.5% property tax state, with average insurance:

  • Principal + interest: $2,661
  • Property tax (1/12 of $7,500/year): $625
  • Homeowners insurance: $150
  • Total monthly PITI: $3,436

Your "mortgage" is really a $2,661 loan payment plus a $775 bundled tax and insurance escrow.

Extra payments and prepayment

Adding even a small extra amount to principal each month has a huge effect because the extra reduces the balance interest is calculated on.

On our $400K, 7%, 30-year example: adding $200/month extra to principal pays off the loan in 25 years instead of 30 and saves about $110,000 in total interest. Adding $500/month cuts the term to about 20 years and saves around $220,000.

Check for prepayment penalties

Most modern US mortgages do not have prepayment penalties, but some still do. Read your loan documents before making extra payments to make sure your bank credits them correctly.

Common questions

How is mortgage interest calculated?

Monthly interest = current balance × (annual rate / 12). It is recalculated each month on the new lower balance, which is why your principal portion slowly grows over the life of the loan.

What is APR?

APR (Annual Percentage Rate) is the interest rate plus most loan fees, expressed as a yearly rate. It is always higher than the quoted interest rate because it includes origination fees, points, and mortgage insurance. Use APR when comparing loans from different lenders — it normalizes the total cost.

Should I pay points?

A point is a fee of 1% of the loan amount paid upfront in exchange for a lower rate (typically 0.25% off). On a $400K loan, 1 point costs $4,000 upfront. It is worth it if you keep the loan long enough to recoup the upfront cost in lower monthly payments — usually 4-6 years.

How much house can I afford?

Rule of thumb: total housing costs (PITI) should be under 28% of gross monthly income. A household earning $10K/month should keep PITI under $2,800. Some banks allow up to 35% but you will feel it.

What is a mortgage amortization schedule?

A month-by-month table showing how each payment splits between interest and principal, and what your remaining balance is. Lenders provide it on request, or our Mortgage Calculator generates one automatically.

Why are mortgages 30 years?

Historical accident, mostly. The 30-year fixed mortgage became the US standard after the New Deal (1934 FHA reforms). Most other countries use shorter terms (UK: typically 25 years and re-fixed every 2-5 years; Germany: 10-25 years). The 30-year US loan is uniquely long among developed economies.

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