Loan Repayment Calculator

This page is for planning the timeline of a loan after the payment amount is known or can be calculated. It estimates total repayment, interest paid, principal paid, payoff time, and the effect of an optional extra monthly payment. The loan payment calculator focuses on the installment due each period; the loan interest calculator focuses on scheduled interest cost. This repayment calculator goes one step further by simulating the balance month by month until it reaches zero.

The form assumes a fixed-rate amortizing loan. It starts with a loan amount or current balance, a term in years, a nominal annual interest rate, a compounding frequency, and an optional extra monthly payment. It does not model adjustable rates, skipped payments, deferment, escrow, taxes, insurance, late fees, or prepayment penalties. If the loan is a mortgage with escrow and housing-specific costs, compare with the mortgage calculator. If the question is whether a payment fits income, use the debt-to-income calculator.

How the payoff simulation works

First, the calculator converts the annual rate and compounding frequency into an effective monthly rate. Then it calculates the scheduled payment that would amortize the loan over the entered term. If you enter an extra monthly payment, that amount is added to the scheduled payment. The calculator then loops month by month. Each month, interest is calculated on the current balance. The payment covers that interest first, and the rest reduces principal. The loop stops when the balance is effectively paid off or if the payment is not large enough to reduce principal.

This simulation is why the payoff time can be shorter than the original term. Extra principal reduces the balance earlier, so future interest is calculated on a smaller amount. The savings line appears only when an extra payment is entered, following the stated calculation.

Formula

The effective monthly rate is:

$\text{monthly rate} = (1 + \frac{\text{annual rate}}{100 \cdot \text{compound frequency}})^{\frac{\text{compound frequency}}{12}} - 1$

The scheduled payment is:

$\text{scheduled payment} = \frac{\text{principal} \cdot \text{monthly rate} \cdot (1 + \text{monthly rate})^{\text{months}}}{(1 + \text{monthly rate})^{\text{months}} - 1}$

The actual monthly repayment is:

$\text{monthly repayment} = \text{scheduled payment} + \text{extra monthly payment}$

Each simulated month follows:

$\text{interest} = \text{balance} \cdot \text{monthly rate}$

$\text{principal paid} = \min(\text{balance}, \text{monthly repayment} - \text{interest})$

$\text{new balance} = \text{balance} - \text{principal paid}$

For a zero-rate loan, the scheduled payment is principal divided by months.

Worked example

Take a $10,000 balance, 10-year term, 7.5% annual interest rate, monthly compounding, and no extra monthly payment. The term creates 120 scheduled months. Monthly compounding makes the effective monthly rate 7.5 divided by 100 and divided by 12, or 0.00625. The scheduled payment is $118.70, so the monthly repayment is also $118.70 because the extra payment is $0.

The month-by-month simulation produces total amount repaid of $14,244.21. Interest paid is $4,244.21, principal paid is $10,000, and payoff time is 10 years 0 months. Those are the default no-extra-payment results. If the same borrower adds $100 per month, the monthly repayment becomes $218.70, the balance is paid off in 55 months, total repayment falls to $11,813.80, interest paid falls to $1,813.80, and interest saved versus the original schedule is $2,430.42. The calculator shows the savings item only in that extra-payment case.

APR, compounding, and payoff quotes

The rate field is treated as the nominal annual interest rate. The compounding dropdown then converts it to a monthly rate. Many consumer disclosures use APR to compare credit costs, but APR and note-rate compounding are not always identical. If a payoff quote from your lender differs from this estimate, timing is often the reason: lenders may calculate interest through a payoff date, add unpaid fees, or include daily interest after the last statement.

Tips for using repayment estimates

• Confirm that extra money will be applied to principal, not held for the next bill.
• Keep an emergency fund before sending all spare cash to a low-rate loan.
• Compare interest savings with any prepayment penalty.
• Recalculate after a refinance, deferment, skipped payment, or large one-time principal payment.
• Pair the result with the budget calculator to make sure the faster payoff remains sustainable.

For shared debts, save the inputs with the date you ran them. A payoff plan is easier to discuss when everyone can see the assumed balance, rate, term, and extra payment amount.

This calculator is informational and not financial advice. It cannot replace a lender payoff statement or review the legal terms of your loan.

Sources

• Consumer Financial Protection Bureau, What is the difference between a loan interest rate and the APR? — consumer explanation of APR and interest rates.
• Consumer Financial Protection Bureau, Loan Estimate explainer — comparison framework for loan costs.
• Federal Reserve, Consumer Credit - G.19 — official consumer-credit data context.