Monthly Payment Calculator

{

Reviewed by: David Chen, CFA
David is a Chartered Financial Analyst with over 15 years of experience in personal finance and loan amortization, helping individuals understand and manage their debt obligations.

This 4-in-1 Monthly Payment calculator helps you understand your loan. Enter any three variables—Loan Amount, Annual Rate, Loan Term, or Monthly Payment—and we will solve for the fourth.

Loan Amount ($) (P)

Annual Rate (%) (R)

Loan Term (Years) (T)

Monthly Payment ($) (M)

Monthly Payment (Amortization) Formula

Solve for Monthly Payment (M):
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]

Solve for Loan Amount (P):
P = M [ (1 + i)^n – 1 ] / [ i(1 + i)^n ]

Solve for Loan Term (n):
n = -ln(1 – (P * i) / M) / ln(1 + i)

Solve for Rate (i):
*No direct formula. Solved iteratively.*

Formula Source: Investopedia

Formula Variables

(M) Monthly Payment: The fixed amount paid each month (Principal & Interest).
(P) Loan Amount: The total principal amount borrowed.
(i) Monthly Interest Rate: The annual rate divided by 12 (i.e., R / 12 / 100).
(n) Number of Payments: The total number of payments (Term in Years * 12).
(ln) Natural Logarithm: A mathematical function used to solve for the term (n).

Related Calculators

What is a Monthly Payment?

A monthly payment, in the context of a loan, is the fixed amount a borrower is required to pay each month to the lender. This payment is typically “amortizing,” meaning each payment is split into two parts: a portion that pays down the principal (the amount you borrowed) and a portion that covers the interest (the cost of borrowing the money).

At the beginning of the loan, a larger portion of your payment goes toward interest. As you continue to make payments and the principal balance decreases, the interest portion shrinks, and more of your payment goes toward paying down the principal. This calculator helps determine this exact payment amount based on the loan’s size, interest rate, and term.

How to Calculate Monthly Payment (Example)

Identify Your Variables
Let’s say you have a $300,000 loan (P) at a 6% annual rate (R) for 30 years (T).
Convert to Monthly Figures
First, find the monthly interest rate (i): 6% / 12 months / 100 = 0.005. Next, find the total number of payments (n): 30 years * 12 months/year = 360.
Calculate the Numerator
The first part of the formula is `P * i * (1 + i)^n`.
$300,000 * 0.005 * (1 + 0.005)^360`
$1,500 * (1.005)^360`
$1,500 * 6.022575...` = $9,033.86
Calculate the Denominator
The second part is `(1 + i)^n – 1`.
(1.005)^360 - 1`
6.022575... - 1` = 5.022575...
Find the Monthly Payment (M)
Divide the numerator by the denominator:
M = $9,033.86 / 5.022575...`
M = $1,798.65

Frequently Asked Questions (FAQ)

Why does my monthly payment change if I only change the term?

The loan term dictates how long you have to repay the principal. A shorter term (e.g., 15 years) means you must pay back the principal faster, resulting in a higher monthly payment. A longer term (e.g., 30 years) spreads the principal over more payments, making each payment smaller but usually resulting in more total interest paid over the life of the loan.

Can I solve for the interest rate if I know my payment?

Yes. If you input your Loan Amount, Loan Term, and desired Monthly Payment, this calculator will solve for the Annual Rate you would need to secure to achieve that payment. This is useful for knowing what rate to shop for.

Does this monthly payment include taxes and insurance (PITI)?

No. This calculator determines the Principal and Interest (P&I) portion of your payment. Your total monthly housing payment (often called PITI) will also include property taxes, homeowners’ insurance, and potentially Private Mortgage Insurance (PMI), which are escrowed by your lender.

How can I find the loan amount I can afford?

Enter your desired Monthly Payment, the current Annual Rate you qualify for, and your desired Loan Term (e.g., 30 years). The calculator will solve for the Loan Amount (P) you can afford based on those numbers.

}