Reviewed and Fact-Checked by: David Chen, CFA
Use this **Mortgage Interest Rate Calculator** to quickly determine the annual interest rate of your loan, based on the principal amount, the monthly payment you make, and the total loan term in years.
Mortgage Interest Rate Calculator
Calculated Annual Interest Rate
This rate is necessary for your amortization schedule.
Mortgage Interest Rate Calculator Formula
The calculation relies on the Present Value of an Annuity formula, where the Loan Amount is the present value, and the monthly payments form the annuity.
$$P = A \times \left[ \frac{1 – (1 + i)^{-N}}{i} \right]$$
Where:
- P: Principal Loan Amount
- A: Periodic (Monthly) Payment
- i: Periodic Interest Rate (i.e., Annual Rate / 12)
- N: Total Number of Payments (Term in Years × 12)
Formula Source: Bankrate Amortization | Investopedia PV of Annuity
Variables Used
Understanding the components used in the calculation is crucial for accurate results:
- Loan Amount (P): The initial amount borrowed from the lender.
- Monthly Payment (A): The fixed amount paid each month to cover both principal and interest.
- Loan Term (Y): The total duration (in years) over which the loan is scheduled to be repaid.
- Annual Interest Rate (R): The calculated yearly rate, expressed as a percentage.
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What is a Mortgage Interest Rate?
The mortgage interest rate is the cost of borrowing the principal amount, expressed as a percentage of the loan balance. It is essentially the price the lender charges for the risk and opportunity cost of providing the capital. This rate is critical because it dictates how much of your monthly payment goes toward interest versus the principal balance over the life of the loan.
In the U.S., mortgage rates are typically quoted as an Annual Percentage Rate (APR). For calculation purposes, this annual rate is divided by 12 to determine the periodic (monthly) interest rate, which is then applied to the remaining loan balance each month. The rate you qualify for depends heavily on factors like your credit score, down payment size, and the current economic environment.
How to Calculate Mortgage Interest Rate (Example)
Since solving for the rate requires an iterative financial calculator, here is a breakdown of the inputs for the calculation:
- Identify the Variables: For a $250,000 loan over 30 years with a $1,500 monthly payment, we have $P = 250,000$, $Y = 30$, and $A = 1,500$.
- Determine Total Payments (N): Calculate the total number of payments: $N = 30 \text{ years} \times 12 \text{ months/year} = 360$.
- Set up the Function: Define the function to solve: $f(i) = 250,000 – 1,500 \times \left[ \frac{1 – (1 + i)^{-360}}{i} \right]$.
- Iterative Solving: The calculator uses numerical analysis (the bisection method) to find the specific value of $i$ that makes $f(i)$ equal to zero.
- Annualize the Rate: Once the monthly rate ($i$) is found, multiply it by 12 and 100 to get the Annual Interest Rate ($R = i \times 12 \times 100$).
Frequently Asked Questions (FAQ)
The interest rate is the cost of borrowing the principal. The Annual Percentage Rate (APR) includes the interest rate plus other costs, such as lender fees, mortgage insurance, and closing costs, giving you a more complete picture of the annual cost of the loan.
The interest rate ($i$) is embedded in the exponent of the amortization formula, making it impossible to isolate algebraically. It requires iterative numerical techniques, like the bisection method or Newton’s method, to find the approximate value.
Your calculated monthly payment (A) only covers principal and interest (P&I). However, if you have an escrow account, your total out-of-pocket payment will also include property taxes and homeowner’s insurance (PITI).
If the monthly payment (A) is less than the monthly interest accrued on the loan ($P \times i$), the loan will never amortize. The calculator will identify this as an impossible scenario and return an error.