Principal & Interest Calculator
Understanding Principal and Interest Calculations
Calculating the principal and interest components of a loan is fundamental to understanding your repayment obligations. When you take out a loan, such as a mortgage, auto loan, or personal loan, your monthly payment is typically divided into two parts: the principal and the interest.
Principal: This is the original amount of money you borrowed. Each payment you make reduces the principal balance of the loan.
Interest: This is the cost of borrowing money. It's calculated as a percentage of the outstanding principal balance. Lenders charge interest to make a profit on the money they lend you.
How the Calculation Works
The most common type of loan repayment schedule is an amortizing loan, where each monthly payment is the same amount. However, within that fixed payment, the proportion allocated to principal and interest changes over time.
Early in the loan term, a larger portion of your payment goes towards interest because the outstanding principal balance is high. As you continue to make payments, the principal balance decreases, and consequently, a larger portion of your subsequent payments goes towards reducing the principal.
The formula to calculate the fixed monthly payment (M) for an amortizing loan is:
$M = P \left[ \frac{i(1+i)^n}{(1+i)^n – 1} \right]$
Where:
- $M$ = Monthly Payment
- $P$ = Principal Loan Amount
- $i$ = Monthly Interest Rate (Annual Rate / 12)
- $n$ = Total Number of Payments (Loan Term in Years * 12)
Once the monthly payment is determined, the calculation for each month is as follows:
- Interest Paid This Month: Outstanding Principal Balance * Monthly Interest Rate ($i$)
- Principal Paid This Month: Total Monthly Payment ($M$) – Interest Paid This Month
- New Principal Balance: Previous Principal Balance – Principal Paid This Month
Why This Calculator is Useful
This calculator helps you understand:
- The total monthly payment you can expect.
- How the interest and principal portions of your payment are allocated, especially in the early stages of a loan.
- The impact of different loan amounts, interest rates, and terms on your overall repayment.
By using this tool, you can make more informed financial decisions regarding borrowing and ensure you have a clear picture of your loan's financial structure.