Mortgage Calculator

The Mortgage Calculator turns a home price, down payment, rate, and term into the numbers a buyer actually lives with: the monthly principal-and-interest payment, the full PITI-style monthly total with property tax, insurance, and HOA, the total interest over the life of the loan, and a year-by-year amortization schedule showing the balance fall.

How It Works

The loan amount is the price minus the down payment. The monthly payment comes from the standard amortization formula, where r is the monthly rate (annual rate / 12) and n is the number of monthly payments:

$M=P\cdot\frac{r(1+r)^{n}}{(1+r)^{n}-1}$

Each month, interest is charged on the current balance and the rest of the payment reduces principal, which is why early payments are almost all interest and late payments almost all principal. Property tax and insurance are divided by 12 and added with HOA fees to form the total monthly payment. At a 0% rate the payment is simply principal divided by months.

Parameters

| Input | Required | Meaning | |---|---|---| | Home price | Yes | Purchase price | | Down payment | Yes | Cash paid upfront; the rest is the loan | | Term (years) | Yes | 30 and 15 are the common terms | | Interest rate | Yes | Annual nominal rate | | Property tax / insurance (annual) | No | Added to the monthly total | | HOA fees (monthly) | No | Added as entered |

Worked example

A $400,000 home with$80,000 down leaves a $320,000 loan. At 6$1,918.56 a month**. Add property tax of $4,800 a year ($400 a month), insurance of $1,800 a year ($150), and a $50 HOA fee, and the total monthly payment is **$2,518.56**. Over the 360 payments you would pay $690,682 of principal and interest, of which **$370,682 is interest**: more than the amount borrowed, the defining fact of long-term amortization. The schedule makes the shape visible: the first payment splits $1,600.00 of interest against just$318.56 of principal, and across the whole first year you pay about $19,093 of interest and only$3,930 of principal. The crossover, where principal first exceeds interest in each payment, does not arrive until well into the loan's second decade.

The three levers, priced

Term: the same $320,000 at 6$2,700.34 a month** but only **$166,062 of total interest**, saving about$204,620 against the 30-year schedule in exchange for $781.78 more each month. **Extra payments:** adding just$200 a month to the 30-year loan clears it in about 283 months (23 years 7 months) and saves roughly **$92,845 of interest**, because every extra dollar attacks principal directly and removes its interest from all remaining months. **Rate:** at 5$1,717.83; at 7% it rises to about $2,128.93, so a single point of rate is worth roughly$200 a month and about $74,000 of lifetime interest on this loan, which is why rate shopping among lenders routinely beats haggling over small seller concessions. Run your own figures through all three levers before deciding what to optimize; households differ in which constraint (monthly cash flow, lifetime cost, payoff date) actually binds.

Reading the amortization schedule

The yearly schedule groups each year's principal, interest, cumulative interest, and ending balance. Three patterns to look for: how slowly the balance moves early (after five years of the example loan, only about $22,200 of principal is gone from$320,000 despite $115,100 of payments); the equity acceleration in the final decade, when most of each payment is principal; and the refinance question the schedule answers implicitly, since refinancing restarts the interest-heavy early years on the remaining balance, a new loan only wins if its rate advantage repays the restart plus closing costs within the time you will actually keep it (the Refinance vs Recast Calculator on this site prices exactly that comparison).

What the calculator leaves out

It models a fixed-rate, fully amortizing loan with monthly payments. It does not include PMI (typically required below 20% down until equity builds), closing costs, escrow true-ups when taxes or insurance rise, HOA increases, adjustable-rate resets, biweekly payment plans, or prepayment penalties. The tax and insurance figures are the ones you enter spread evenly; lenders' escrow estimates differ and are adjusted annually. For the affordability question that precedes this one (how much house the income supports), the How Much House Can I Afford calculator works the same mathematics backwards from a payment budget.

Frequently Asked Questions

Why is so much of the early payment interest?

Interest is charged on the outstanding balance, and the balance is largest at the start. The payment is fixed, so as the balance falls the interest portion shrinks and the principal portion grows by the same amount. Nothing is being front-loaded by the lender beyond that arithmetic; it is the amortization formula itself.

Does a larger down payment change the rate maths?

It changes the principal, not the formula: every $10,000 of down payment on this example's terms removes about$60 a month and roughly $11,580 of lifetime interest. It can additionally remove PMI and unlock better rate tiers, effects outside this calculator but often larger than the payment effect.

Should I choose the 15-year term if I can afford it?

On pure interest cost, yes by a wide margin, and the rate on 15-year loans is usually lower still, widening it further. The honest counterweights are flexibility (the higher payment is obligatory in bad months too; a 30-year loan with voluntary extra payments mimics the 15-year in good times and breathes in bad ones, at the price of discipline) and opportunity cost of the extra cash. The calculator prices both schedules so the trade is explicit.