Calculadora de empréstimos e financiamento

How a fixed-rate loan payment is calculated

A fixed-rate loan — a mortgage, car loan, or personal loan — is repaid in equal monthly instalments. Each payment is split between interest (the cost of borrowing the outstanding balance for one month) and principal (the part that actually reduces your debt). The amount that keeps the payment constant for the whole term comes from the standard amortization formula:

M = P × r × (1 + r)ⁿ / ((1 + r)ⁿ − 1)

Here P is the principal, r is the monthly interest rate (the annual APR divided by 12, then by 100), and n is the total number of monthly payments (years × 12). This calculator uses exactly that formula. When the rate is zero it falls back to the obvious case, P / n, since there is no interest to compound.

A worked example

Take a $300,000 loan at 5.5% APR over 30 years — the tool's default. First convert the inputs: the monthly rate is 5.5 ÷ 100 ÷ 12 = 0.0045833, and the number of payments is 30 × 12 = 360. Plug those in:

• (1 + r)ⁿ = 1.0045833³⁶⁰ ≈ 5.1937
• Numerator: 300,000 × 0.0045833 × 5.1937 ≈ 7,141.8
• Denominator: 5.1937 − 1 = 4.1937
• Monthly payment: 7,141.8 ÷ 4.1937 ≈ $1,703.37

Over 360 months that is about $613,213 paid in total, of which roughly $313,213 is interest — more than the original loan. This is the single most important thing the calculator reveals: on a long mortgage you frequently pay more in interest than you borrowed.

Why early payments are almost all interest

The amortization table this tool generates shows each month's split. In month one of the example above, interest is 300,000 × 0.0045833 = $1,375, so only $1,703.37 − $1,375 = $328 goes to principal. The balance barely moves. As the balance shrinks, the interest portion shrinks with it and the principal portion grows, so by the final years almost the entire payment is principal. This front-loading of interest is why selling or refinancing early in a mortgage builds little equity, and why extra payments are so powerful at the start.

The amortization schedule, row by row

Each row of the schedule is computed in sequence: the month's interest is the current balance times the monthly rate; the principal is the fixed payment minus that interest; the new balance is the old balance minus the principal. Repeat 360 times and the balance lands on (near) zero at the final payment. Reading the table top to bottom shows your equity building slowly then accelerating — a curve, not a straight line.

The power of extra payments

Because interest each month is charged only on the remaining balance, any dollar you pay above the scheduled amount goes straight to principal and erases all the future interest that dollar would otherwise have accrued. Adding even $100 a month to the example loan shaves several years off the term and saves tens of thousands in interest, because every early principal reduction compounds forward through the rest of the schedule.

What this calculator does not include

• Taxes and insurance. The result is principal and interest (P&I) only. A real mortgage payment often bundles property tax and homeowners insurance into escrow — the full figure lenders call PITI — which can add hundreds of dollars a month.
• PMI and HOA fees. Private mortgage insurance (required on many low-down-payment loans) and homeowners-association dues are separate again.
• Closing costs and points. Up-front fees change the true cost of borrowing but not the monthly P&I.
• Variable rates. The math assumes the rate is fixed for the whole term; an adjustable-rate loan would recompute the payment whenever the rate resets.

Practical tips

• Compare term lengths. A 15-year loan has a higher monthly payment but dramatically less total interest than a 30-year loan at the same rate — run both and look at the "total interest" figure, not just the monthly number.
• Watch the rate's leverage. A small change in APR moves the payment more than people expect on a large balance. Re-run the numbers for every quote you receive.
• Budget for PITI, not P&I. Add your local property-tax rate and an insurance estimate before deciding what you can afford.

Every figure is computed in your browser from the three numbers you enter — nothing is sent to a server, so you can model as many scenarios as you like privately.