Loan Payment Calculator

Reviewed by: **Dr. Sarah Willis, Financial Economist**
Expert in macroeconomics and consumer credit risk modeling with a focus on sustainable lending practices.

The **Loan Payment Calculator** is the most essential tool for any borrowing decision. It quickly calculates the required monthly payment based on the principal amount, interest rate, and loan term. This powerful calculator can also solve for the missing variable: Principal, Payment, Rate, or Term.

Instructions: Enter values for any three of the four loan parameters (P, F, V, Q) to solve for the missing one.

Loan Parameters

Principal Amount ($P$) – [P]

Monthly Payment ($M$) – [F]

Annual Interest Rate (%) ($R$) – [V]

Loan Term (Months) ($N$) – [Q]

Loan Amortization Formula

The standard formula used to calculate the Monthly Payment ($M$) for an amortizing loan:

Monthly Payment ($M$):

$$M = P \left[ \frac{i(1+i)^n}{(1+i)^n – 1} \right]$$

Where $P = \text{Principal, } i = R/1200 \text{ (monthly rate), and } n = \text{Term in Months}$.

Formulas for solving $P$, $R$, and $N$ are derived from this core equation.

Formula Source: Investopedia: Monthly Payment

Variables Explained (P, F, V, Q – Loan Parameters)

$P$ (Principal Amount): The initial sum of money borrowed, or the balance remaining.
$F$ (Monthly Payment): The fixed amount paid monthly to service the loan (interest + principal).
$V$ (Annual Rate): The annual interest rate applied to the loan balance.
$Q$ (Loan Term): The total duration of the loan, measured in months.

Related Loan Planning Calculators

Use these related tools to plan your borrowing:

What Determines a Loan Payment?

A loan payment, often referred to as the monthly installment, is the fixed amount a borrower must pay each month to the lender. This payment covers two distinct components: a portion that pays down the principal (the original amount borrowed) and a portion that covers the interest accrued since the last payment.

The monthly payment amount is determined by the three primary variables: the principal, the interest rate, and the loan term. Due to the compounding effect, where interest is charged on the diminishing principal, the interest portion of the payment is highest at the beginning of the loan and lowest at the end. This concept is formalized in the amortization schedule.

Understanding the exact monthly payment is crucial for budgeting and assessing the financial feasibility of a loan before committing to the debt.

How to Calculate a Loan Payment (Example)

Calculate the Monthly Payment for a \$20,000 loan at 7.5% APR for 5 years (60 months):

Step 1: Calculate Monthly Interest Rate ($i$)
$i = 7.5\% / 1200 = 0.00625$
Step 2: Calculate the Amortization Factor
The factor $D$ is $D = (1+i)^n / ((1+i)^n – 1)$. For $n=60$, the factor is approximately $0.0200375$.
Step 3: Calculate Monthly Payment ($M$)
$M = P \times i \times D$. $M = \$20,000 \times 0.00625 \times 0.0200375 \approx \mathbf{\$400.75}$.

Frequently Asked Questions (FAQ)

Does the monthly payment change?

For a fixed-rate loan, the monthly payment remains the same over the entire term. For an Adjustable-Rate Mortgage (ARM), the rate (and thus the payment) can change after the initial fixed period.

Does this include escrow or insurance?

No. This calculator determines the Principal and Interest (P&I) portion of a loan payment only. Additional costs like property taxes (escrow) and insurance are added separately to calculate the total payment.

How much of my payment goes to principal?

Initially, a large portion covers the interest. As the loan amortizes (pays down), the principal portion increases, and the interest portion decreases. This crossover typically happens around the halfway point of the loan term.

Why is my bank’s payment slightly different?

Banks may use slightly different compounding conventions (daily vs. monthly) or round to different decimal points. They also may include fees like loan origination fees into the principal amount, slightly inflating the payment.

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