How Do I Calculate Interest on a Loan

Calculate Loan Interest

Understanding Loan Interest

Calculating the interest on a loan is a fundamental aspect of personal finance, whether you're taking out a mortgage, a car loan, a personal loan, or using a credit card.

Simple Interest vs. Compound Interest

Loans typically accrue interest in one of two ways: simple or compound. For most standard installment loans (like mortgages and car loans), compound interest, often calculated on a monthly basis, is applied. This calculator focuses on the total interest paid over the life of a loan using a common amortization formula.

How Interest is Calculated on a Loan

The total interest paid over the life of a loan is the difference between the total amount repaid and the original principal amount borrowed. While the exact calculation can be complex, it's primarily driven by three factors:

• Principal Amount: The initial amount of money borrowed. A larger principal means more interest will be paid.
• Annual Interest Rate: The percentage charged by the lender for borrowing the money. This is usually expressed as a yearly rate.
• Loan Term: The duration over which the loan must be repaid. A longer term generally means more total interest paid, even if monthly payments are lower.

The Amortization Formula (Simplified Concept)

For standard installment loans, monthly payments are calculated using an amortization formula designed to pay off both the principal and interest over the loan's term. The total interest paid is then derived from these monthly payments.

The formula for the monthly payment (M) is:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]

Where:

• P = Principal loan amount
• i = Monthly interest rate (Annual Rate / 12)
• n = Total number of payments (Loan Term in Years * 12)

Once the monthly payment (M) is calculated, the total amount repaid is M * n. The total interest paid is then (M * n) – P.

Example Calculation:

Let's say you take out a loan with the following details:

• Principal (P): $20,000
• Annual Interest Rate: 6%
• Loan Term: 5 years (which is 60 months)

First, we convert the annual rate to a monthly rate (i): 6% / 12 months = 0.06 / 12 = 0.005

The number of payments (n) is 5 years * 12 months/year = 60.

Using the monthly payment formula:

M = 20000 [ 0.005(1 + 0.005)^60 ] / [ (1 + 0.005)^60 – 1] M = 20000 [ 0.005(1.005)^60 ] / [ (1.005)^60 – 1] M = 20000 [ 0.005 * 1.34885 ] / [ 1.34885 – 1 ] M = 20000 [ 0.00674425 ] / [ 0.34885 ] M ≈ $386.64

Total amount repaid = Monthly Payment * Number of Payments = $386.64 * 60 = $23,198.40

Total Interest Paid = Total Amount Repaid – Principal = $23,198.40 – $20,000 = $3,198.40

Why Use This Calculator?

Understanding the total interest burden helps you make informed decisions about borrowing. You can use this calculator to:

• Compare loan offers from different lenders.
• Estimate the cost of borrowing for various purchase decisions.
• Understand the impact of interest rates and loan terms on your overall cost.