Check the offer, repayment alternatives and related plans
Use the comparison guide to audit APR, fees, term and total cost, then open another calculator when the decision involves several debts, property or saving first.
How much of the repayment is principal, interest and optional acceleration?
The model separates the amount borrowed from the interest cost and shows whether the extra payment meaningfully shortens the loan.
Change the loan amount, term, rate or extra payment and the repayment picture updates automatically.
Extra-payment payoff check – scheduled loan vs your current plan
This comparison keeps the loan amount, rate and original term unchanged. It then compares the scheduled loan with the same loan plus your extra monthly principal payment. It is useful for seeing whether a small extra outflow materially changes the payoff date or lifetime interest.
| Scenario | Monthly outflow | Payoff time | Total interest | Total paid |
|---|---|---|---|---|
| — | ||||
Principal crossover check – when does principal become at least half of the payment?
On long amortizing loans, early payments can be dominated by interest because the outstanding balance is still high. This check finds the first payment where the principal portion is at least as large as the interest portion. It also shows whether your extra principal payment moves that milestone earlier.
| Scenario | Crossover payment | Approximate time | Interpretation |
|---|---|---|---|
| — | |||
Amortization schedule for your current plan
The schedule below follows the regular payment plus the extra monthly amount you entered. Each payment first covers the modelled monthly interest; the remainder reduces principal. The last payment is adjusted for cent rounding so the balance reaches zero without an artificial extra month.
Show the full payment-by-payment amortization schedule
| Payment | Payment amount | Principal | Interest | Interest to date | Remaining balance |
|---|---|---|---|---|---|
| — | |||||
How the monthly loan payment is calculated
For a standard fixed-rate fully amortizing loan, the scheduled payment is chosen so that repeated equal payments reduce the balance to zero over the stated number of months. Let P be the principal, r the monthly interest rate and n the number of monthly payments.
The annual interest rate is converted to a monthly rate by dividing the decimal annual rate by 12. A 7% annual rate therefore becomes 0.07 ÷ 12 per month in this model. When the annual rate is 0%, the interest formula would divide by zero, so the calculator uses the simpler relationship P ÷ n.
After the scheduled payment is known, the amortization schedule is built one month at a time. Monthly interest equals the current balance multiplied by the monthly rate. The part of the payment left after interest is the principal reduction.
Principal repaid = payment − interest
New balance = opening balance − principal repaid
An optional extra monthly payment is added to the principal-reducing part of the cash flow. The model keeps the scheduled payment unchanged and uses the extra amount to reduce the balance faster, which is why future interest can fall.
For a quick manual comparison before entering exact values, use the Loan Payment Table per $1,000 borrowed.
Interest rate vs APR – use the right input
The annual interest rate and APR are related but they are not automatically interchangeable. The interest rate is the rate used to calculate interest on the outstanding principal. APR can incorporate additional loan charges. Because this calculator models the payment from principal, rate and term, the input should be the contractual interest rate used for the payment calculation.
If you enter an APR that includes origination or other lender fees as though it were the loan interest rate, the payment estimate can be distorted. Use APR as a broader comparison measure when comparing loan offers, but use the actual interest rate when reproducing a standard principal-and-interest payment.
Where should the loan inputs come from?
| Input | Good source | What to verify |
|---|---|---|
| Loan amount | Loan offer, contract or current principal balance. | Use the amount actually being financed, not the purchase price if a down payment reduces borrowing. |
| Interest rate | Loan disclosure or lender quote. | Confirm that it is the interest rate used for payment calculations rather than an APR that includes fees. |
| Term | Loan agreement or offer. | Use the remaining term when analysing an existing balance rather than the original term if part of the loan has already been repaid. |
| Extra payment | Your own repayment plan and lender rules. | Confirm that extra money can be applied to principal without a penalty or a different allocation rule. |
Does the result look realistic?
Three quick checks catch many input mistakes. First, at a positive interest rate the scheduled monthly payment must be greater than the first month of interest, otherwise the balance would not amortize normally. Second, a longer term should usually lower the monthly payment but increase lifetime interest if the rate and principal stay unchanged. Third, adding an extra principal payment should not increase the payoff time or total interest in this model.
At 0% interest, the check becomes even simpler: monthly payment × number of months should equal the loan amount, apart from cent rounding in the final payment. If the result violates one of these relationships, recheck the rate, term and amount before using the estimate.
Practice problems – solve first, then reveal the answer
These are calculation exercises, not presets. Work them out first and use Show answer only to check your method.
Exercise 1 – zero-interest loan
A $12,000 loan has a 0% interest rate and a 2-year term. What is the monthly payment and total interest?
There are 24 payments, so $12,000 ÷ 24 = $500. With a 0% rate, every dollar of each payment reduces principal.
Exercise 2 – standard amortizing loan
A $20,000 loan carries 6.5% annual interest for 5 years. Estimate the scheduled monthly payment and total interest with no extra payments.
The monthly rate is 0.065 ÷ 12 and n = 60. The payment formula gives about $391.32. The schedule totals about $23,479.41, of which $20,000 is principal and about $3,479.41 is interest.
Exercise 3 – effect of an extra payment
A $35,000 loan is repaid over 6 years at 7.2%. The scheduled payment is about $600.08. What happens if $100 extra is paid toward principal every month?
In this model the payoff falls from 72 to about 60 months. Total interest falls from about $8,205.96 to $6,736.32, a saving of about $1,469.63. Actual lender treatment of extra payments must still be checked.
What affects the repayment most?
Principal: borrowing more increases both the payment and the amount on which interest is charged. Interest rate: a higher rate increases the cost of carrying the balance. Term: stretching repayment across more months usually lowers the monthly payment but gives interest more time to accumulate. Extra principal: paying down the balance earlier can reduce future interest because subsequent interest is calculated on a smaller balance in this model.
The cheapest-looking monthly payment is therefore not automatically the lowest-cost loan. A longer term can make the monthly cash flow easier while producing a much larger lifetime interest total.
Common mistakes when estimating loan payments
- Using APR as the interest-rate input even though APR includes fees that are not part of the amortization rate.
- Comparing only the monthly payment and ignoring total interest and total amount paid.
- Using the original term for an existing loan when the goal is to model the remaining balance and remaining months.
- Assuming every extra payment is automatically applied to principal.
- Using this fixed-rate model for a variable-rate loan without modelling future rate changes.
- Expecting a mortgage principal-and-interest estimate to include taxes, insurance or mortgage insurance.
- Ignoring a balloon payment, precomputed-interest structure or other contract feature that prevents normal full amortization.
- Treating the calculator as a lender quote instead of checking the actual disclosure and repayment rules.
For finance and business students: understanding an amortizing loan step by step
A fixed-payment loan is a strong finance-math exercise because the payment stays almost constant while the composition of that payment changes over time. The key is to distinguish the cash payment from the two things it finances: interest for the current period and reduction of outstanding principal.
1. Define the variables
Let P be the original principal, r the annual interest rate as a decimal, i the monthly rate, n the number of monthly payments and PMT the scheduled monthly payment.
2. Solve the annuity equation for the payment
The present value of all scheduled future payments must equal the amount borrowed in the simplified model. Rearranging the present-value annuity equation gives:
If i = 0, use PMT = P ÷ n instead.
3. Split each payment into interest and principal
Interest is calculated from the opening balance for that month. The rest of PMT reduces principal. Because the balance falls over time, the interest component normally falls and the principal component rises.
Principalt = PMT − Interestt
Balancet = Balancet−1 − Principalt
4. Worked student exercise
Problem: A $100,000 fixed-rate loan has a 7% annual interest rate and a 20-year term. First calculate the scheduled monthly payment. Then compare the normal loan with a plan that adds $100 to principal each month.
- Monthly rate: 7% ÷ 12 = 0.5833333% = 0.005833333.
- Number of payments: 20 × 12 = 240.
- Payment factor denominator: 1 − (1.005833333)−240 ≈ 0.752398.
- Exact payment: 100,000 × 0.005833333 ÷ 0.752398 ≈ $775.2989, displayed as $775.30 per month.
- First-month interest: $100,000 × 0.005833333 = $583.33.
- First-month principal at the scheduled payment: $775.30 − $583.33 ≈ $191.97.
- No-extra schedule: the loan lasts 240 months and modelled total interest is about $86,071.45.
- With $100 extra per month: planned outflow is $875.30. The loan pays off in about 189 months instead of 240.
- Interest with the extra plan: about $65,226.02, saving about $20,845.42 in this model.
- Time saved: 51 months, or about 4 years 3 months.
- Principal crossover: without extra principal becomes at least as large as interest around payment 122; with the $100 extra plan this happens around payment 71.
5. Sanity checks for an amortization problem
At 0%, total payments should equal the principal. With a positive rate, total paid should exceed principal. If the term gets longer while principal and rate stay fixed, the scheduled monthly payment should normally fall while lifetime interest rises. Adding extra principal should reduce the balance faster in this model. Finally, the interest portion of a fixed payment should generally trend downward as the outstanding balance falls.
When this calculator is not enough
This page models a fixed-rate, monthly, fully amortizing loan with interest calculated from the outstanding balance. It does not model adjustable rates, interest-only periods, balloon payments, payment holidays, daily simple-interest timing, precomputed interest, changing fees, origination costs, taxes, insurance or payment penalties.
Extra payments are assumed to reduce principal immediately. Real lenders may require specific instructions, may advance the due date instead, may have prepayment restrictions or may use a different accrual convention. If the loan agreement has any of those features, use the lender's official schedule or disclosure as the controlling source.
Use the result as an educational repayment estimate, not as personalized financial advice or a binding lender quote.