Loan Repayment Calculator — See Your True Interest Cost Over Time

Calculate loan payments, total interest, and remaining balance using explicit assumptions and inspectable arithmetic.

Most loan calculators show you a payment and move on.
This calculator shows where the money actually goes.

Enter your loan amount, interest rate, term, and payment frequency to see:

Your required payment per period
The total interest paid over the life of the loan
How your remaining balance declines over time
A full amortization table you can inspect line by line

No advice. No optimization.
Just the arithmetic behind a standard fixed-rate loan.

Inputs

Loan amount (principal)

Annual interest rate

Amortization term (years)

Payment frequency

No start date, extra payments, fees, or taxes are modeled. This calculator focuses on the arithmetic of a standard fixed-rate, fully amortizing loan.

Results

Total paid
$—

Total interest
$—

Payment per period

$—

Number of payments

—

With these inputs: a $P loan at r% annual interest over term years, paid frequency.

Balance and principal over time

Shows the remaining principal curve over time, with the area below split into interest and principal portions of each payment.

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Amortization Schedule

Period	Payment	Interest	Principal	Remaining balance
Total	$—	$—	$—	$0.00

How this loan repayment calculator works

This calculator models a fixed-rate, fully amortizing loan.

Each payment consists of:

Interest, calculated on the remaining balance
Principal, which reduces the balance

Early payments are mostly interest.

Later payments are mostly principal.

The total interest cost depends on rate, term, and payment frequency.

The math used (no hidden assumptions)

Let:

P = loan amount (principal)
r = annual interest rate (as a decimal)
m = payments per year (12 monthly, 26 biweekly, 52 weekly)
i = r / m = interest rate per payment
N = years × m = total number of payments

The payment per period is calculated as:

Payment = P * [ i(1+i)^N ] / [ (1+i)^N - 1 ]

If the interest rate is zero, payments are simply:

Payment = P / N

For each payment:

Interest = remaining balance × i
Principal = payment − interest
New balance = old balance − principal

The amortization table, charts, and totals are all derived from this same calculation.

Assumptions and limitations

Fixed interest rate for the entire loan term
Interest compounds at the payment frequency selected
No fees, penalties, insurance, or taxes included
Payments are rounded to cents for display
Final balance is clamped to zero to avoid rounding noise

This calculator does not give advice or recommendations.

It shows the arithmetic implied by your inputs.

Disclaimer: All content on The Long Math — including articles, essays, calculators, tools, or any other material — is provided solely for educational and informational purposes and does not constitute financial, tax, legal, or investment advice. Any results or projections are based on simplified models, assumptions, and user-supplied inputs and may not reflect real-world outcomes. You are responsible for evaluating the accuracy and applicability of the information provided and for conducting your own due diligence. Before making financial decisions, consult a qualified professional.