Created by Tibor Pál, PhD candidate
Reviewed by
Wei Bin Loo and Steven Wooding
Based on research by
Cipra T. Financial and Insurance Formulas; 2006
Last updated:
Jan 18, 2024
- How to calculate interest on a loan
- What is the loan interest formula?
- How to use the loan interest calculator
- FAQ
The loan interest calculator (or interest calculator on loan) is a simple tool that helps you estimate the interest on your loan. In addition, you can check the loan's balance including periodic interest and principal payments in the loan amortization schedule.
In the following article, we show you how to calculate interest on a loan, and you can read some interesting details in our FAQ.
To learn more about loan amortization, check our amortization calculator.
How to calculate interest on a loan
The best way to understand how interest is calculated on a loan is to introduce it with a real-life example.
Let's assume you are considering obtaining a loan for a car purchase, so you decide to turn to a bank that offers you a personal loan of 10,000 dollars with 6% interest, repaid monthly in 10 years with the same compounding frequency. You can easily insert this data into our loan interest calculator:
- Loan balance: $10,000
- Loan term: 10
- Interest rate: 6%
- Payment frequency: Monthly
- Compounding frequency: Monthly
As a first step, you need to compute the equivalent rate, which is adjusted for compounding frequency. Since, in the present case, the payment frequency and the compounding frequency coincide, the equivalent rate equals the given interest rate. If you want to check the formula for this calculation, visit our equivalent rate calculator.
Calculate the periodic rate (i) by dividing the annual interest rate by the number of payments in a year. In our case, it is 0.06 / 12 = 0.005.
Compute the total number of payments (or periods, n) required to repay the loan principal. In our case, it is 12 × 10 = 120.
Apply the below formula for calculating the periodic payment.
P=1−(1+i)−ni×A
where:
- P — Periodic payment;
- A — Loan balance or principal;
- i — Periodic rate; and
- n — Number of payments or periods.
In our case, the periodic (monthly) payment is $111.02.
Calculate the total payment by multiplying the periodic payment by the number of payments. Therefore, the total payment is 111.02 × 120 = $13,322.46.
The interest payment is the difference between the total payment and the principal balance (or loan amount). That is, the interest on the above loan is 13,322.46 – 10,000 = $3,322.46.
What is the loan interest formula?
The loan interest formula can be formulated in the following way.
Interest = A - (i × A × n)/(1 – (1 + i)-n)
where:
- A is the loan balance or principal;
- i is the periodic equivalent rate; and
- n is the number of payments or periods.
How to use the loan interest calculator
You need to follow the below simple steps to apply for our loan interest calculator:
- Input the loan balance you plan to borrow. It will be the principal, which needs to be repaid.
- Provide the loan term.
- Provide the interest rate.
- Set the payment frequency.
- Choose the compounding frequency, which will be the timing of capitalization of the interest (the unpaid amount of interest added to the loan's principal balance).
You can also follow the accumulation of the total interest on the chart of balances and the periodic or annual interest payments in the amortization schedule displayed below the main results.
FAQ
What is the interest of a $10,000 loan with a 6% rate?
The interest of a $10,000 loan with a 6% rate with ten years loan term repaid monthly is $3,322.46.
How can I calculate loan interest?
Follow the below steps to calculate loan interest.
Calculate the periodic rate (i) by dividing the annual interest rate by the number of payments in a year (n).
Calculate the total payment (P) by multiplying the periodic rate (i) with the loan amount (A) and the number of payment (n) and then divide it by the factor of 1 – (1 + i)-n.
Finally, calculate the loan interest by subtracting the loan amount from the total payment (interest = P - A).
Why are interest rates are increasing?
Interest rates are increasing due to monetary policy intervention responding to high inflation rates. The higher interest rates reduce aggregate demand as fewer consumers take a loan, which eventually can lead to disinflation and lower inflation expectations.
Tibor Pál, PhD candidate
