finance calculatorFormula, worked examples and edge cases shown
A mortgage payment is level, but what it is made of changes every month. Early payments are almost entirely interest; late payments are almost entirely principal. Enter the loan, the rate and the term to see the payment, the total cost, and how the balance comes down.
What this calculator does
Someone is looking at a house price and a quoted rate and wants to know the monthly payment, and often wants to compare a 15-year term against a 30-year term to see what the shorter one saves.
What the monthly payment is actually made of
A mortgage payment is the same amount every month, which makes it feel like a fixed cost. It is not a fixed cost in substance. Every month the lender charges interest on whatever balance is outstanding, and the rest of your payment goes to reducing that balance. Because the balance is at its largest at the start, the interest charge is at its largest at the start.
On a $300,000 loan at 6.5% over thirty years, the payment is $1,896.20. In the first month the interest alone is $1,625.00 — so only $271.20 of that payment actually reduces what you owe. By the final year almost the whole payment is principal. This is not a trick or a penalty; it is what "interest on the outstanding balance" means.
The practical consequence is that paying extra early is worth far more than paying extra late. An extra $100 in the first month saves interest on that $100 for the entire remaining term. The same $100 in the final year saves almost nothing. If you expect to have spare cash at some point, the earlier the better.
Why a shorter term costs more per month but much less overall
A fifteen-year loan on the same $300,000 at the same 6.5% has a payment of $2,613.32 — $717.12 more per month. In exchange, the total interest falls from $382,633.47 to $170,397.98. You pay $212,235.49 less for the same house.
That is the whole trade: a higher monthly commitment in return for a much lower total. Whether it is the right trade depends on whether the higher payment is comfortably affordable, because the risk of a shorter term is that a bad year makes the payment impossible. A thirty-year loan that you overpay voluntarily gives you most of the interest saving with the option to stop overpaying.
The rate matters less than the term at these magnitudes. Dropping from 6.5% to 5.5% on a thirty-year $300,000 loan saves roughly $200 a month; dropping from thirty years to fifteen costs $717 more a month but saves over $200,000 in total interest.
What this calculator leaves out
The payment shown here is principal and interest only. A real monthly housing cost also includes property tax, homeowners insurance, and often mortgage insurance if the down payment was below twenty percent. Those are collected with the payment in an escrow account, which is why the figure your lender quotes is usually noticeably higher than this one.
It also excludes closing costs, which are paid once at the start and can run to several percent of the loan, and it assumes the rate never changes. An adjustable-rate mortgage will reset, and the payment after the reset is not predictable from the initial rate alone.
Finally, this is a repayment calculation, not an affordability calculation. A lender will approve a payment that a household cannot comfortably sustain, because the lender's exposure ends if the house is sold. Yours does not.
How to use this calculator
Enter the amount you are actually borrowing. Subtract your down payment from the purchase price first — the loan amount is what the interest is charged on.
Put in the interest rate from your quote. Use the nominal rate rather than the APR if you want to match a lender's own amortisation schedule.
Set the term. Run it once at thirty years and once at fifteen, and compare both the monthly payment and the total interest.
Read the total interest line as the real cost of borrowing. On a long loan at a normal rate it usually exceeds the amount you borrowed.
The formula
M = P × i ÷ (1 − (1 + i)^−N), where i = APR ÷ 12 and N = 12 × years
M
the level monthly payment
P
the amount borrowed
i
the monthly interest rate — the annual rate divided by 12
N
the total number of monthly payments
The payment is level, but the split between interest and principal is not: each month the interest is the current balance multiplied by i, and whatever is left of the payment reduces the balance. Because the balance falls slowly at first, the interest share falls slowly too.
Worked examples
Example 1 — a thirty-year loan
You borrow $300,000 at 6.5% over thirty years. The monthly payment is $1,896.20. Over 360 payments you hand over $682,633.47 in total, of which $382,633.47 is interest — more than the amount you borrowed. That headline is the single most useful number on this page, and it is why the term is worth arguing about before the rate is.
Example 2 — the same loan over fifteen years
The identical $300,000 at the identical 6.5%, but repaid over fifteen years. The payment rises to $2,613.32, which is $717.12 a month more. Total paid over the term is $470,397.98, of which $170,397.98 is interest — a saving of $212,235.49 against the thirty-year version. Nothing about the rate changed; the entire saving comes from the balance being outstanding for half as long.
Example 3 — a smaller loan at a lower rate
Borrow $250,000 at 5.25% over fifteen years and the payment is $2,009.69. Total interest is $111,744.97 against a total outlay of $361,744.97. Compare it with Example 1 and the difference is not mostly the lower rate: it is that $250,000 is repaid over fifteen years instead of $300,000 over thirty. Both inputs are doing work, and the term is doing more of it.
Year by year
What each year of a $300,000 loan at 6.5% over 30 years actually does
Year
Interest paid
Principal paid
Balance left
1
$19,401.27
$3,353.18
$296,646.82
2
$19,176.70
$3,577.74
$293,069.08
3
$18,937.10
$3,817.35
$289,251.73
4
$18,681.44
$4,073.01
$285,178.72
5
$18,408.66
$4,345.79
$280,832.93
6
$18,117.62
$4,636.83
$276,196.10
7
$17,807.08
$4,947.37
$271,248.73
8
$17,475.75
$5,278.70
$265,970.03
9
$17,122.22
$5,632.23
$260,337.81
10
$16,745.02
$6,009.43
$254,328.38
11
$16,342.56
$6,411.89
$247,916.49
12
$15,913.14
$6,841.31
$241,075.18
13
$15,454.97
$7,299.48
$233,775.70
14
$14,966.11
$7,788.34
$225,987.36
15
$14,444.51
$8,309.94
$217,677.42
16
$13,887.98
$8,866.47
$208,810.95
17
$13,294.17
$9,460.28
$199,350.68
18
$12,660.60
$10,093.85
$189,256.83
19
$11,984.60
$10,769.85
$178,486.98
20
$11,263.32
$11,491.13
$166,995.85
21
$10,493.74
$12,260.71
$154,735.14
22
$9,672.62
$13,081.83
$141,653.30
23
$8,796.50
$13,957.95
$127,695.36
24
$7,861.71
$14,892.74
$112,802.62
25
$6,864.32
$15,890.13
$96,912.49
26
$5,800.13
$16,954.32
$79,958.16
27
$4,664.66
$18,089.79
$61,868.38
28
$3,453.16
$19,301.29
$42,567.08
29
$2,160.51
$20,593.94
$21,973.15
30
$781.30
$21,973.15
$0.00
Edge cases worth knowing
An interest rate of 0%
The payment is simply the loan divided by the number of payments — $300,000 over 360 months is $833.33. The formula divides by the rate, so an implementation that does not special-case this returns infinity.
A term of 0 years
There are no payments, so the payment is zero. This is a degenerate case rather than a realistic one, but the form allows it and a blank result would look like a bug.
A very large loan or a very long term
The arithmetic holds, but the interest total grows faster than the loan does — a $1,000,000 loan at 6.5% over 30 years costs about $1.28 million in interest alone. Long terms are expensive in a way that does not feel expensive month to month.
Frequently asked questions
How is a monthly mortgage payment calculated?
Multiply the loan amount by the monthly interest rate, then divide by 1 minus (1 + monthly rate) raised to the power of the negative number of payments. The monthly rate is the annual rate divided by twelve. This produces a level payment that pays the loan down to exactly zero at the end of the term.
Why is most of my early payment interest?
Because interest is charged on the outstanding balance, and the balance is at its highest at the start. On a $300,000 loan at 6.5%, the first payment of $1,896.20 contains $1,625.00 of interest and only $271.20 of principal. As the balance falls, the interest charge falls with it and a larger share of each payment goes to principal.
Is a 15-year mortgage better than a 30-year?
It costs much less in total interest — on $300,000 at 6.5% it saves $212,235.49 — but the payment is $717.12 a month higher. The right answer depends on whether the higher payment stays affordable through a bad year. A 30-year loan you overpay voluntarily gives most of the saving while keeping the option to stop.
Does this include taxes and insurance?
No. The figure here is principal and interest only. Property tax, homeowners insurance and mortgage insurance are collected alongside the payment in escrow, which is why the amount your lender quotes is higher than the number on this page.
Related calculators
Compound Interest CalculatorA mortgage is compounding seen from the borrower's side: the balance falls instead of rising, but each month's interest is worked out the same way.
Savings Goal CalculatorThe mirror image for the other direction of travel — what a loan costs per month, against what a savings plan needs per month.
Simple Interest CalculatorNeeded before comparing quotes: some car and short-term finance is quoted at simple interest, which is not comparable to a mortgage rate at the same percentage.