Use the **Loan Amortization Calculator** to determine your required monthly payment, total loan principal, annual interest rate, or loan term. This tool uses the core amortization formula. Input any three known financial variables to solve for the missing fourth component.
Loan Amortization Calculator
Step-by-Step Calculation:
Loan Amortization Formula:
Monthly Payment $(M) = P_{loan} \times \frac{r(1+r)^n}{(1+r)^n – 1}$
Where $P_{loan}$ is the Principal (F), $r$ is the monthly rate (P/1200), and $n$ is the total months (V x 12).
Formula Source: Investopedia (Amortization Formula)
Key Variables Explained:
- **Loan Principal (P / F):** The starting amount of the loan (e.g., mortgage, auto loan). (Currency)
- **Annual Interest Rate (R / P):** The yearly interest rate charged on the loan. (Percentage)
- **Loan Term (N / V):** The total duration of the loan in years. (Years)
- **Monthly Payment (M / Q):** The constant monthly amount paid to the lender. (Currency)
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- Mortgage Refinance Savings Calculator
- Mortgage Down Payment Calculator
- Rent vs. Buy Analysis Tool
- Home Equity Line of Credit (HELOC) Estimator
What is Loan Amortization?
Loan amortization is the process of gradually paying off debt over time in scheduled installments. In the early stages of a loan (like a mortgage), a larger portion of the monthly payment is allocated to interest, while in the later stages, a larger portion goes toward reducing the principal.
The amortization calculation is critical because it determines the fixed monthly payment (M) required to pay off the principal and interest exactly over the specified loan term (N). This calculator allows you to reverse-engineer any component of the amortization equation.
How to Calculate Monthly Payment (Example)
- Determine the Loan Principal (P). Assume $\text{P}=\$200,000$.
- Determine the Annual Interest Rate (R). Assume $R=6\%$.
- Determine the Loan Term (N). Assume $N=30$ years.
- Convert to monthly rate ($r$) and total periods ($n$): $r = 0.06 / 12 = 0.005$, $n = 30 \times 12 = 360$.
- The Monthly Payment $(M)$ is calculated using the formula, approximately $\mathbf{\$1,199.10}$.
Frequently Asked Questions (FAQ)
How does the Loan Term affect the total interest paid?
A longer loan term (e.g., 30 years) results in a lower monthly payment, but the borrower pays significantly more total interest over the life of the loan compared to a shorter term (e.g., 15 years).
Can this calculator solve for the interest rate?
Yes. Since the interest rate (R) cannot be isolated algebraically, the calculator uses iterative methods (like the Bisection Method) to find the precise rate that satisfies the amortization equation, given the other three variables.
What is the difference between Amortization and Simple Interest?
Amortization is the process of paying off a loan over time with structured payments. Simple interest is the method used to calculate the interest accrued on the outstanding principal at any given point (P x r x t). The amortization formula integrates simple interest into a fixed payment schedule.
Are property taxes and insurance included in this calculation?
No. This calculator only determines the principal and interest (P&I) portion of the monthly mortgage payment. It excludes escrow items like property taxes and homeowner’s insurance.