Monthly Payment Calculator

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Reviewed by: **David Chen, CFA, Loan Structuring Expert**
Certified Financial Analyst with 15+ years of experience in consumer and commercial debt underwriting and amortization.

The **Monthly Payment Calculator** is the most essential tool for budgeting. It quickly determines your required monthly payment based on the loan principal, annual interest rate, and term. This calculator can also solve for the missing Principal, Rate, or Term when any three variables are provided.

Instructions: Enter values for any three of the four core parameters (Principal, Rate, Term, or Payment) to solve for the missing one.

Loan Parameters

Loan Principal ($P$) – [Q]

Monthly Payment ($M$) – [F]

Annual Interest Rate ($R$) (%) – [P]

Loan Term ($N$) (Years) – [V]

Loan Payment Formula

The calculation is based on the standard Annuity Formula, solving for $M$:

Monthly Payment ($M$):

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

Loan Principal ($P$):

$$P = M \times \frac{(1+i)^n – 1}{i(1+i)^n}$$ Formula Source: Investopedia

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

$P$ (Loan Principal, $Q$): The total loan amount borrowed (or calculated).
$M$ (Monthly Payment, $F$): The fixed periodic payment (or calculated).
$R$ (Annual Interest Rate, $P$): The yearly nominal interest rate.
$N$ (Loan Term, $V$): The duration of the loan in years.

Related Loan Affordability Calculators

Determine your borrowing power and payment structure:

What is a Loan Payment?

A **Loan Payment** (or monthly installment) is the fixed periodic amount a borrower agrees to pay to a lender over the life of a loan. In amortizing loans (like most mortgages, car loans, and personal loans), each payment consists of two parts: a portion that covers the accrued interest and a portion that reduces the remaining loan principal. Early in the loan’s term, the interest portion is large, but as the principal balance decreases, the interest portion shrinks, and more of the fixed payment goes toward reducing the principal.

Calculating the payment is crucial for borrowers to ensure the loan fits their budget. This calculator uses the core amortization formula to accurately determine this monthly amount or to reverse-engineer any of the other three primary factors.

How to Calculate Loan Payment (Example)

Assume a Loan Principal ($P$) of \$100,000, an Annual Rate ($R$) of 6%, and a Term ($N$) of 20 years. We solve for the Monthly Payment ($M$):

Step 1: Determine Monthly Rate and Total Periods
Monthly rate $i = 0.06 / 12 = 0.005$. Total periods $n = 20 \times 12 = 240$.
Step 2: Calculate the Payment Factor
$$Factor = \frac{i(1+i)^n}{(1+i)^n – 1} \approx 0.007164$$
Step 3: Calculate the Monthly Payment
$M = P \times Factor = \$100,000 \times 0.007164 \approx \mathbf{\$716.43}$.

The required **Monthly Payment** is $\mathbf{\$716.43}$.

Frequently Asked Questions (FAQ)

How much of my first payment goes to principal?

In the first month, the interest paid is $P \times i$. The amount going to principal is $M – Interest Paid$. This principal portion is usually the smallest amount of any payment.

What is the difference between APR and interest rate?

The APR (Annual Percentage Rate) is typically higher than the nominal interest rate because it includes fees. For most amortization calculations, you use the nominal interest rate, but for comparing loan costs, the APR is the better figure.

Can I solve for the Loan Principal using this calculator?

Yes. Enter your desired Monthly Payment ($M$), the Interest Rate ($R$), and the Loan Term ($N$) while leaving the Principal field empty. The calculator will solve for the maximum loan amount you can borrow.

Why is my loan payment higher than the calculator shows?

For mortgage loans, your total payment often includes PITI (Principal, Interest, Taxes, and Insurance) paid into an escrow account. This calculator only calculates the P&I portion (Principal and Interest).

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