Fully Amortized Loan Calculator

Loan Payment Formula:

\[ PMT = P \times \frac{r \times (1 + r)^n}{(1 + r)^n - 1} \]

Monthly Payment (PMT):

Total Payment:

Total Interest:

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1. What is a Fully Amortized Loan?

A fully amortized loan is a type of loan where regular payments (usually monthly) consist of both principal and interest, calculated so that the loan will be paid off completely by the end of the term. Common examples include mortgages and auto loans.

2. How Does the Calculator Work?

The calculator uses the standard loan payment formula:

\[ PMT = P \times \frac{r \times (1 + r)^n}{(1 + r)^n - 1} \]

Where:

\( PMT \) — Monthly payment amount
\( P \) — Principal loan amount
\( r \) — Monthly interest rate (annual rate ÷ 12)
\( n \) — Total number of payments (loan term in years × 12)

Explanation: The formula accounts for the time value of money, calculating equal payments that cover both interest and principal over the loan term.

3. Understanding Loan Amortization

Details: In early payments, a larger portion goes toward interest. As the loan matures, more of each payment is applied to the principal. This calculator shows the fixed payment amount that fully pays off the loan by the end of the term.

4. Using the Calculator

Tips: Enter the principal amount, annual interest rate (as a percentage), and loan term in years. The calculator will show your fixed monthly payment, total repayment amount, and total interest paid.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between amortized and interest-only loans?
A: Amortized loans pay down principal with each payment, while interest-only loans require payments that only cover interest during the initial period.

Q2: How does a longer loan term affect payments?
A: Longer terms reduce monthly payments but increase total interest paid over the life of the loan.

Q3: Can I see an amortization schedule?
A: This calculator shows the summary totals. For a detailed payment-by-payment breakdown, use an amortization schedule calculator.

Q4: Are there loans that don't fully amortize?
A: Yes, balloon loans have payments based on a longer term but require a large final payment to pay off the remaining balance.

Q5: How accurate is this calculator?
A: It provides accurate estimates for fixed-rate loans. Actual loans may have additional fees or insurance costs not included here.