Data Source and Methodology

This calculator uses the standard, industry-accepted formula for calculating the payment on an amortized loan, also known as the "present value of an annuity" formula. This is the same formula used for mortgages, auto loans, and most fixed-rate personal loans.

All calculations are based rigorously on this mathematical principle.

The Formula Explained

The periodic payment (M) is calculated using the following formula:

$$ M = P \frac{r(1+r)^n}{(1+r)^n - 1} $$

Where each variable represents:

  • $M$ = Your periodic payment
  • $P$ = The principal loan amount
  • $r$ = The periodic interest rate (your annual rate divided by 12)
  • $n$ = The total number of payments (your term in years multiplied by 12)

Glossary of Variables

Term Definition
Loan Amount (P) The total amount of money you are borrowing.
Annual Interest Rate (APR) The yearly cost of the loan, expressed as a percentage.
Loan Term (n) The total time you have to repay the loan, typically in years or months.
Monthly Payment (M) The fixed amount you pay each month, which includes both principal and interest.
Principal (Payment) The portion of your monthly payment that goes towards reducing your loan balance.
Interest (Payment) The portion of your monthly payment that pays for the cost of borrowing.
Total Interest The cumulative sum of all interest paid over the entire life of the loan.
Amortization The process of paying off debt over time in regular installments of principal and interest.

How It Works: A Step-by-Step Example

Let's say you take out a $25,000 loan for 5 years at an annual interest rate of 7.5%.

  1. Identify the variables:
    • $P$ (Principal) = $25,000
    • Annual Rate = 7.5% (or 0.075)
    • Term = 5 years
  2. Calculate the periodic rate (r) and total payments (n):
    • $r$ (monthly rate) = 0.075 / 12 = 0.00625
    • $n$ (total payments) = 5 years * 12 months/year = 60 payments
  3. Plug the values into the formula:

    $$ M = 25000 \times \frac{0.00625 \times (1+0.00625)^{60}}{(1+0.00625)^{60} - 1} $$

  4. Solve the equation:

    $$ M = 25000 \times \frac{0.00625 \times (1.45329...)}{(1.45329...) - 1} $$

    $$ M = 25000 \times \frac{0.009083...}{0.45329...} $$

    $$ M = 25000 \times 0.020038... $$

  5. Final Monthly Payment:

    $$ M = \$500.95 $$

Frequently Asked Questions (FAQ)

What's the difference between installment and simple interest loans?

This calculator is for installment (amortized) loans. In this model, each payment is split between principal and interest. The interest is calculated based on the *remaining loan balance*. As you pay down the balance, the interest portion of your payment decreases, and the principal portion increases.

A simple interest loan (less common for personal loans) calculates interest based on the *original principal* for the entire loan term. The interest does not compound or change based on the balance.

How can I pay off my loan faster?

You can pay off an installment loan faster by making extra payments. The most common methods are:

  • Extra Principal Payments: Adding an extra amount to your monthly payment. Ensure your lender applies this extra amount directly to the principal balance.
  • Bi-weekly Payments: Making half-payments every two weeks. This results in 26 half-payments, or 13 full monthly payments per year, effectively adding one extra payment annually.

Both methods reduce your principal balance faster, which in turn reduces the total interest you pay over the life of the loan.

What is APR (Annual Percentage Rate)?

APR, or Annual Percentage Rate, is the yearly interest rate charged on the loan. It is a crucial number for comparing loan offers, as a lower APR generally means a less expensive loan.

Does this calculator include fees?

No. This calculator determines your payment based only on the principal, interest rate, and term. It does not account for one-time origination fees, annual fees, or potential late fees, which could be part of your loan agreement. Always read the loan terms carefully.

What is a loan amortization schedule?

The amortization schedule (shown in the table above) is a complete list of every payment you will make over the life of the loan. It breaks down each individual payment into its interest and principal components, showing you exactly how your balance decreases with every payment until it reaches zero.

Tool developed by Ugo Candido.

Financial methodology and content verified by the CalcDomain Editorial Board.

Last review for accuracy: