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Principal vs Interest
About the Mortgage Calculator
A mortgage payment is the fixed monthly amount that pays off a loan balance over a set number of years while covering interest on whatever is still owed. The number is fully determined by four inputs: how much you borrow, the interest rate, the length of the term, and how often interest compounds. Everything else people associate with a housing payment — property tax, homeowners insurance, mortgage insurance, HOA dues — sits outside the loan and is added on top.
That distinction matters more than it sounds. The figure this calculator produces is principal and interest only, usually written as P&I. A lender quoting your "monthly payment" will often quote PITI instead, which bundles taxes and insurance into an escrow account. On a typical American home those extras add roughly 20% to 30% on top of P&I, so a $2,275 loan payment can arrive as a $2,850 bill. Comparing a P&I figure from one source against a PITI figure from another is the single most common way people mis-plan a home purchase.
The reason a fixed payment works at all is that its composition shifts over time. Early on, almost all of it is interest, because interest is charged on a large remaining balance. As the balance falls, the interest portion shrinks and the principal portion grows, even though the total stays flat. This is why paying a mortgage for five years often retires far less principal than people expect, and why extra payments made early are worth dramatically more than the same money paid later.
Formula
M = P × [ r(1 + r)^n ] / [ (1 + r)^n − 1 ]
- M
- Monthly principal and interest payment
- P
- Loan principal — the purchase price minus the down payment
- r
- Monthly interest rate, i.e. the annual rate divided by 12
- n
- Total number of monthly payments — the term in years times 12
The formula is the standard annuity payment equation solved for the payment amount. It answers the question: what constant monthly sum, discounted back at the loan rate, has a present value exactly equal to the amount borrowed?
The critical conversion is the rate. A 6.5% annual rate becomes r = 0.065 / 12 ≈ 0.0054167 per month, and a 30-year term becomes n = 360. Feeding an annual rate into a monthly formula is the error that produces payment estimates roughly ten times too large, and it is worth checking first whenever a result looks absurd.
Note that (1 + r)^n appears in both numerator and denominator. That term is the growth factor of the loan over its full life — at 6.5% over 30 years it equals about 6.99, meaning a dollar left uncompensated for the whole term would grow sevenfold. The formula is essentially dividing the loan into 360 equal slices of that growth.
Worked Examples
A $450,000 home with 20% down over 30 years
You are buying at $450,000, putting $90,000 down, and have been quoted 6.5% on a 30-year fixed loan. You want the principal-and-interest payment and the lifetime interest cost.
Result: $2,275.44 per month in principal and interest
Over 360 payments that comes to $819,160, of which $459,160 is interest — more than the original loan. In the very first payment, $1,950 goes to interest and only $325 to principal.
The same loan at 15 years instead of 30
Same $360,000 at the same 6.5%, but on a 15-year term. People often assume the payment roughly doubles. It does not.
Result: Payment rises 38% ($2,275 → $3,136), total interest falls 55% ($459,160 → $204,478)
Halving the term saves $254,682 in interest for an extra $861 per month. The asymmetry exists because the shorter loan spends far less time carrying a large balance.
What one percentage point of rate is worth
Same $360,000 over 30 years, but the quote comes in at 7.5% rather than 6.5%.
Result: One extra point costs $241.73 a month and $87,022 over the life of the loan
A single rate point moves lifetime cost by roughly a quarter of the original purchase price. This is why shopping three or four lenders reliably outperforms negotiating on price by a similar percentage.
How to Use the Result
What the payment does not include
Principal and interest is the loan. The bill is usually larger. Budget separately for each of the following, because none of them is affected by your rate or term:
- —Property tax — typically 0.5% to 2.2% of assessed value per year depending on the state, billed monthly into escrow. On a $450,000 home at 1.2% that is $450 a month.
- —Homeowners insurance — commonly $100 to $250 a month, and rising fast in wildfire and coastal-storm regions.
- —Private mortgage insurance (PMI) — required on conventional loans when the down payment is under 20%, typically 0.3% to 1.5% of the loan per year. It can usually be cancelled once you reach 20% equity, but the lender will not do it automatically.
- —HOA or condo dues — not escrowed, not tax-deductible, and able to rise with a board vote.
- —Maintenance — no lender charges it, but a common planning rule is 1% of the home value per year.
Why extra principal payments work so unevenly
An extra dollar applied to principal eliminates all future interest that dollar would have accrued. Because interest compounds over the remaining term, that saving depends entirely on when the payment is made.
On the $360,000 example, $200 a month extra from the first payment retires the loan roughly six years early and saves well over $100,000. The identical $200 a month started in year 20 saves a small fraction of that, because there is little remaining term for the avoided interest to accumulate over.
One practical consequence: if you are choosing between a 15-year loan and a 30-year loan that you promise yourself you will overpay, the 15-year loan is only better if the lower rate it usually carries outweighs the loss of flexibility. The overpayment itself produces the same amortization either way.
Fixed versus adjustable, and what the formula assumes
This calculation assumes a fixed rate for the entire term. An adjustable-rate mortgage (ARM) only behaves this way during its initial fixed period — a 5/1 ARM holds the rate for five years, then re-amortizes annually against an index.
To evaluate an ARM, run the calculation twice: once at the teaser rate to see the initial payment, and once at the lifetime cap to see the worst case you are agreeing to. If the capped payment is unaffordable, the teaser rate is not a discount, it is a deferral.
Edge Cases and Common Mistakes
A 0% interest rate breaks the formula
When r = 0 the denominator (1 + r)^n − 1 becomes zero and the expression is undefined. The correct payment in that case is simply P / n. Seller financing and some family loans genuinely run at 0%, so this is not purely theoretical.
Biweekly payments are not the same as monthly
A biweekly schedule produces 26 half-payments a year, which equals 13 monthly payments rather than 12. The extra payment is what shortens the loan, not the payment frequency. If your lender charges a fee to set this up, making one voluntary extra payment a year achieves the identical result for free.
The final payment rarely matches the others
Payments are rounded to the cent each month, and those roundings accumulate. The last payment is typically a few dollars above or below the standard amount. Any amortization schedule that shows 360 perfectly identical payments has quietly absorbed the difference.
Canadian mortgages compound semi-annually
Canadian fixed-rate mortgages are compounded twice a year by law, not monthly. A 6.5% Canadian mortgage has an effective monthly rate of (1.0325)^(1/6) − 1 ≈ 0.005345, slightly below the 0.0054167 used for a US loan. Using the US convention overstates a Canadian payment by a few dollars a month.
Frequently Asked Questions
Why is my lender quoting a higher payment than this calculator?
Almost certainly because the lender is quoting PITI — principal, interest, taxes and insurance — while this calculates principal and interest only. Ask for the P&I line specifically and the two should match to within a dollar. If they still differ, check whether PMI or a rate buydown is included.
Is APR the same as the interest rate?
No. The interest rate determines your payment. APR folds origination fees, discount points and some closing costs into a single annualized figure, so it is higher than the rate on nearly every loan. Use the interest rate for this calculation and the APR to compare offers against each other.
How much house can I afford from a payment figure?
Lenders generally cap total housing cost at about 28% of gross monthly income and total debt at about 36%. Work backwards from 28% of your gross pay, subtract your estimated taxes and insurance to get an affordable P&I, then solve for the principal that produces it. Note that this is the lender's ceiling, not a recommendation.
Should I put down more than 20%?
Twenty percent is the threshold that removes PMI; beyond that the decision is purely a comparison of returns. Extra down payment earns a guaranteed after-tax return equal to your mortgage rate. At 6.5% that is a strong risk-free return and often beats holding the cash — but it is also money you cannot access without refinancing or selling.
Does making one extra payment a year really cut years off the loan?
Yes, and the effect is large. On the $360,000 at 6.5% example, one extra full payment annually retires the loan roughly four and a half years early and saves around $100,000 in interest, because every extra dollar removes decades of compounding on that dollar.
What happens to my payment if I refinance?
Refinancing starts a new loan with a new term, so the amortization clock resets. Refinancing a 30-year loan into a fresh 30-year loan after five years can lower the payment while increasing lifetime interest, because you return to the interest-heavy start of the curve. Compare total remaining interest, not monthly payment.