Loan Calculator
Model a fixed-rate amortizing loan with independent compounding and repayment frequencies. Calculate the required periodic payment, total interest, total paid, effective annual rate, payoff date, and full amortization schedule, with optional extra principal payments.
Additional
How to use the loan calculator
Enter the loan amount, repayment term, and annual interest rate. Then choose how often the rate compounds and how often payments are made.
For a common monthly installment loan, leave both Compound and Pay back set to Monthly and read the required payment immediately.
If the loan uses a different structure, change either frequency independently. For example, you can model monthly compounding with payments every two weeks.
Open Additional to add extra principal to every scheduled installment or set the first payment date used by the amortization schedule.
Compounding frequency and payment frequency are different
Compounding frequency controls how the entered annual rate is translated into effective growth over one year.
Payment frequency controls how often installments are made. The calculator converts the annual-rate model into an equivalent interest rate for that repayment interval.
These frequencies do not have to match. A loan can therefore be modeled with monthly compounding and biweekly repayments, quarterly compounding and monthly repayments, or another supported combination.
| Setting | What it controls | Supported options |
|---|---|---|
| Compounding frequency | How the entered annual rate is converted into an effective annual rate | Annual, semi-annual, quarterly, monthly, semi-monthly, biweekly, weekly, daily, continuous |
| Pay back frequency | How often installments are made and the rate used for each payment period | Daily, weekly, every 2 weeks, twice monthly, monthly, quarterly, every 6 months, yearly |
How the periodic loan payment is calculated
Once the equivalent rate per payment period is known, a standard amortization formula calculates the equal scheduled installment required to repay the principal over the modeled number of payments.
If the annual interest rate is zero, the calculation is simpler: principal is divided across the scheduled installments.
The final payment can be smaller because the calculator limits it to the exact principal and modeled interest still outstanding.
Why payment frequency changes the numbers
Changing repayment frequency changes both the number of installments and the interest rate associated with each installment period.
For example, five years of monthly payments produces 60 scheduled installments, while five years of biweekly payments produces 130 modeled installments.
The amount of each payment therefore changes even when the loan amount, annual rate, and overall term remain the same.
Why compounding frequency changes the effective annual rate
A stated annual rate can produce different one-year growth depending on how frequently it compounds.
At a 6% nominal annual rate, annual compounding produces a 6% effective annual rate. Monthly compounding produces an effective annual rate of about 6.1678%.
The calculator converts that compounding convention into the equivalent rate needed for whichever repayment frequency you choose.
Continuous compounding uses the exponential limit rather than a fixed number of compounding periods.
A loan's interest rate is not necessarily its APR
The interest-rate input controls the interest mathematics in this amortization model.
APR is a broader borrowing-cost measure that can include certain fees in addition to interest. Because this calculator does not model those fees, entering a fee-inclusive APR as though it were the loan's stated interest rate can produce the wrong payment schedule.
Use the Olivez APR Calculator when the goal is to measure borrowing cost after applicable fees rather than build the note-rate amortization schedule.
Extra payments reduce principal sooner
An extra payment is added to every installment at the selected repayment frequency and applied to principal in the model.
Reducing principal sooner means later interest is calculated from a smaller balance. This can reduce both total interest and the number of payments required.
The calculator runs a baseline schedule without extra principal and compares it with the accelerated schedule so interest saved, payments saved, and the new payoff date are visible.
Check the actual loan agreement or contact the lender before relying on an early-payoff strategy. Payment-allocation rules and prepayment charges can differ.
How to read the total loan cost
Total paid is divided into principal and modeled interest.
Principal is the amount originally borrowed. Interest is the additional amount produced by the modeled rate and repayment schedule.
The colorful cost chart shows their shares of the complete repayment amount, while the payoff chart shows the remaining balance falling as cumulative principal repayment rises.
How to read the amortization schedule
Each row represents one scheduled installment, not necessarily one month.
A monthly loan therefore has monthly rows, a weekly loan has weekly rows, and a biweekly loan has a row for each two-week payment period.
The schedule shows the payment date, total installment, principal, interest, extra principal, and remaining balance.
The exported CSV also includes beginning balance and cumulative principal, interest, and payments.
| Column | Meaning |
|---|---|
| Payment | Amount paid during that repayment period |
| Principal | Amount of the payment that reduces the outstanding balance |
| Interest | Interest charged on the beginning balance for that period |
| Extra | Principal paid above the scheduled installment |
| Balance | Principal remaining after the payment |
What the first payment date does
The first payment date anchors the dates displayed in the amortization schedule and determines the modeled payoff date.
Daily, weekly, and biweekly schedules advance by their corresponding number of days. Monthly, quarterly, semi-annual, and annual schedules advance by calendar months.
The date does not change the equivalent periodic interest rate. The tool does not calculate an irregular first period from the exact number of days between loan funding and the first installment.
Real loans may use a different interest method
This calculator is a generalized fixed-rate amortization model. Actual consumer loans may calculate interest using contract-specific methods.
For example, some loans use simple interest based on the outstanding principal on a daily or monthly basis. Others can use precomputed interest or different payment-posting rules.
That distinction matters especially when making early or irregular payments. Use the lender's agreement or servicing statement when an exact contractual payoff amount is required.
Loan Calculator, APR Calculator, and Mortgage Calculator
Use the Loan Calculator to model scheduled installments, flexible payment frequencies, interest, extra principal, and amortization for a generic fixed-rate loan.
Use the APR Calculator when applicable fees and finance charges need to be incorporated into an annual borrowing-cost measure.
Use the Mortgage Calculator when the calculation also needs mortgage-specific housing costs and home-loan assumptions.
What this calculator does not model
The calculator deliberately focuses on amortized repayment rather than trying to represent every lending product in one form.
It does not model variable rates, balloon payments, interest-only periods, deferred payments, precomputed-interest contracts, refinancing, missed payments, irregular cash flows, taxes, insurance, origination fees, or penalties.
Those structures require different assumptions and, in some cases, different calculation engines.
| Area | Modeled | Not modeled |
|---|---|---|
| Rate model | Entered annual rate converted through the selected compounding frequency | Lender-specific daily simple interest, variable rates, promotional rates, and rate changes |
| Repayment | Equal scheduled installments at the selected payment frequency | Missed, late, partial, deferred, or irregular payments |
| Extra payment | One fixed extra amount applied to principal with every scheduled payment | One-time lump sums, annual extras, and lender-specific allocation rules |
| Borrowing costs | Principal and modeled interest | Origination fees, insurance, taxes, closing costs, add-ons, penalties, and other finance charges |
| Result | Meaning |
|---|---|
| Periodic payment | Scheduled payment required at the selected repayment frequency |
| Number of payments | Modeled installments required to repay the loan |
| Total interest | Sum of modeled interest charges across the repayment schedule |
| Total paid | Principal plus modeled interest across all payments |
| Effective annual rate | One-year rate implied by the entered annual rate and selected compounding frequency |
| Payoff date | Date of the final modeled payment using the selected repayment schedule |
Loan payment and equivalent-rate formulas
The calculator first converts the annual rate and selected compounding convention into an effective rate for each payment period. It then applies the standard amortized-loan payment formula and builds the repayment schedule installment by installment.
- Original loan principal
- Entered annual interest rate as a decimal
- Compounding periods per year
- Scheduled payments per year
- Effective annual rate
- Equivalent interest rate per payment period
- Number of scheduled installments
- Scheduled payment each repayment period
- Outstanding principal before payment t
- Modeled interest during payment period t
- Scheduled principal paid during period t
- Extra principal paid during period t
- Principal balance after payment t
Examples
Standard monthly loan
Loan amount: $100,000; term: 10 years; annual rate: 6%; compound monthly; pay back every month.
The scheduled payment is $1,110.21 per month across 120 modeled payments. Total modeled interest is about $33,224.31 and total paid is about $133,224.31.
Monthly compounding at a 6% nominal annual rate produces an effective annual rate of about 6.1678%.
Biweekly repayments with monthly compounding
Loan amount: $20,000; term: 5 years; annual rate: 6%; compound monthly; pay back every 2 weeks.
The model creates 130 biweekly installments of about $178.22. Total modeled interest is about $3,168.14.
The equivalent rate per two-week payment period is about 0.23046%.
Compare annual and monthly compounding
Loan amount: $100,000; term: 10 years; annual rate: 6%; monthly repayments.
With annual compounding, the modeled monthly payment is about $1,102.25. With monthly compounding, it is about $1,110.21.
The annual-compounding case has a 6% effective annual rate, while monthly compounding produces about 6.1678%.
Add $100 to every monthly payment
Loan amount: $25,000; rate: 7.5%; term: 5 years; monthly compounding and repayment; extra payment: $100 each month.
The scheduled payment is $500.95 and the planned payment is $600.95. The modeled payoff falls from 60 payments to 49, saving 11 payments and about $1,013.70 in interest.
Continuous compounding
Loan amount: $10,000; term: 3 years; annual rate: 5%; continuous compounding; monthly repayments.
The modeled monthly payment is about $299.76 and total modeled interest is about $791.21.
A continuously compounded 5% annual rate corresponds to an effective annual rate of about 5.1271%.
Zero-interest loan
Loan amount: $1,200; term: 1 year; rate: 0%; monthly repayments.
The scheduled payment is $100 per month, total interest is $0, and total paid is $1,200.
Frequently Asked Questions
What is the difference between compounding frequency and payment frequency?
Compounding frequency determines how the annual rate accumulates. Payment frequency determines how often you make installments. The calculator converts the first into an equivalent rate for the second.
Do the compounding and repayment frequencies have to match?
No. They can be selected independently, such as monthly compounding with biweekly repayments.
How is the loan payment calculated when the frequencies differ?
The calculator first converts the entered annual rate and compounding convention into an equivalent rate for one payment period. It then uses that periodic rate in the amortized-loan payment formula.
What does monthly compounding mean?
The entered annual rate is divided into 12 nominal compounding periods. The resulting effective annual rate is then converted to the selected repayment interval.
What is continuous compounding?
Continuous compounding is the mathematical limit of increasingly frequent compounding. The calculator uses an exponential rate conversion for that option.
How many biweekly payments are modeled in a year?
The calculator uses 26 modeled biweekly payments per year.
How many weekly and daily payments are modeled?
Weekly repayment uses 52 modeled payments per year and daily repayment uses 365.
Why can some repayment frequencies reject my loan term?
Quarterly payments require complete three-month periods, semi-annual payments require complete six-month periods, and annual repayments require complete years so the schedule does not end partway through an installment period.
Should I enter the interest rate or APR?
Use the annual interest rate that corresponds to the loan's interest calculation. APR can include additional fees and should not automatically be substituted for the note rate in an amortization schedule.
What is the effective annual rate shown in the result?
It is the one-year rate produced by the entered annual rate and selected compounding frequency.
Why can two loans with the same stated annual rate have different payments?
Different compounding frequencies can produce different effective annual rates. Different repayment frequencies also change the number of installments and the rate associated with each payment period.
How does the extra payment work?
The entered extra amount is added to every scheduled installment and applied to principal in the model.
Does paying principal early always save interest?
It reduces interest in this amortization model because later interest is calculated on a smaller balance. Actual results depend on the lender's interest method, payment-allocation rules, and any prepayment charges.
Why can the final payment be smaller?
The normal scheduled payment is rounded to cents. The final installment is reduced to the exact principal and modeled interest still outstanding.
Does the first payment date change the interest rate?
No. It determines the schedule dates and payoff date. The calculator does not use an irregular day count between funding and the first payment.
Can I use this for a personal loan?
Yes when the loan is a fixed-rate amortizing loan and its interest and repayment conventions can be represented by the available frequency settings.
Can I use this for an auto loan?
It can model a fixed amortized structure, but many auto loans use daily or monthly simple interest. Check the contract before treating the calculator as an exact lender schedule.
Can I use this for a mortgage?
The principal-and-interest calculation may be useful, but the Mortgage Calculator is better when mortgage-specific costs and housing assumptions need to be included.
Does this calculator include loan fees?
No. It models principal and interest. Use the APR Calculator when applicable finance charges need to be incorporated into borrowing-cost analysis.
Can this model balloon, interest-only, or deferred-payment loans?
No. Those structures have different repayment rules and are outside this calculator's fixed-amortization model.
Why might a lender's amortization schedule differ?
A lender may use daily simple interest, exact transaction dates, different rounding, irregular first periods, payment-posting rules, precomputed interest, fees, or other contract-specific methods.
Can I export the amortization schedule?
Yes. The CSV contains every modeled installment with payment date, beginning balance, payment, principal, extra principal, interest, remaining balance, and cumulative totals.