David is a Chartered Financial Analyst and mortgage expert with over 15 years of experience in real estate finance and interest rate analysis.
This 4-in-1 Mortgage Rate calculator helps you understand your loan. Enter any three variables—Loan Amount, Loan Term, Monthly Payment, or Annual Rate—and we will solve for the fourth.
Mortgage Rate Calculator
Mortgage Amortization Formula
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):
*Solved iteratively (no direct formula)
Formula Variables
- (P) Loan Amount (Principal): The total amount of money borrowed.
- (M) Monthly Payment: The fixed amount paid each month for principal and interest.
- (T) Loan Term: The total length of the loan, in years.
- (R) Annual Rate: The nominal annual interest rate for the loan.
- (i) Periodic Rate: The monthly interest rate (R / 12 / 100).
- (n) Number of Payments: The total number of payments (T * 12).
Related Calculators
- Mortgage Principal Calculator
- Mortgage Interest Calculator
- Loan Term Calculator
- Mortgage Payment Calculator
What is a Mortgage Rate?
A mortgage rate, also known as the Annual Percentage Rate (APR), is the interest rate you pay on your home loan. This rate is one of the most critical factors in determining the total cost of your mortgage and the size of your monthly payment. A lower mortgage rate means you pay less in interest over the life of the loan, which can save you tens of thousands of dollars.
Mortgage rates are influenced by a variety of factors, including the broader economy, inflation, and the policies set by the Federal Reserve. Your personal financial profile also plays a huge role. Lenders assess your credit score, debt-to-income (DTI) ratio, loan size, and the size of your down payment to determine the specific rate they will offer you. A higher credit score and a larger down payment typically result in a lower, more favorable mortgage rate.
How to Calculate Your Mortgage Rate (Example)
While you can’t easily calculate your mortgage rate by hand (it requires an iterative algorithm, which this calculator does automatically), you can see how other factors are calculated. Let’s solve for the Monthly Payment (M).
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Identify Your Variables:
– Loan Amount (P): $300,000
– Annual Rate (R): 5.0%
– Loan Term (T): 30 years -
Convert Annual Rate and Term:
– Monthly Interest Rate (i) = 5.0% / 12 months / 100 = 0.004167
– Total Number of Payments (n) = 30 years * 12 months = 360 -
Apply the Formula:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]
M = 300,000 [ 0.004167 * (1 + 0.004167)^360 ] / [ (1 + 0.004167)^360 – 1 ]
M = 300,000 [ 0.004167 * 4.4677 ] / [ 4.4677 – 1 ]
M = 300,000 [ 0.018616 ] / [ 3.4677 ]
M = 300,000 * 0.005369
M = $1,610.86
Frequently Asked Questions (FAQ)
What is the difference between an interest rate and an APR?
The interest rate (or nominal rate) is the direct cost of borrowing money. The Annual Percentage Rate (APR) is a broader measure that includes the interest rate plus other loan fees and costs (like origination fees or mortgage insurance), expressed as an annual percentage. The APR is generally considered the more accurate measure of a loan’s true cost.
How can I get a lower mortgage rate?
You can secure a lower mortgage rate by improving your credit score, making a larger down payment (ideally 20% or more), lowering your debt-to-income (DTI) ratio, and shopping around with multiple lenders to compare offers.
How does the loan term affect my mortgage rate?
Generally, shorter loan terms (like a 15-year mortgage) come with lower interest rates than longer-term loans (like a 30-year mortgage). While your monthly payment will be higher on a 15-year loan, you will pay significantly less in total interest over the life of the loan.
Can I solve for my rate if I know my payment?
Yes. This calculator is designed to do exactly that. If you enter your desired monthly payment, your total loan amount, and the loan term, the calculator will solve for the annual rate you would need to qualify for.