Interest Rate Calculator

About Interest Rate Calculator

Find the interest rate on any fixed-rate loan when you know the principal, monthly payment, and term. The calculator uses Newton's method to work backward from the standard loan formula, giving you the exact annual and monthly rate to two decimal places.

How Is the Interest Rate Found?

The standard loan payment formula is:

M = P x r x (1 + r)^n / ((1 + r)^n - 1)

Normally you plug in P (principal), r (monthly rate), and n (payments) to find M (monthly payment). This calculator does the reverse: given M, P, and n, it finds r. There is no algebraic way to isolate r directly, so the calculator uses Newton's method - an iterative numerical technique that converges on the answer within a fraction of a second.

Worked example: You borrowed $25,000 for a car, pay $489 per month, and the term is 60 months. What is the interest rate?

• The calculator iterates to find: monthly rate = 0.5417%
• Annual rate: 0.5417% x 12 = 6.50%
• Total paid: $489 x 60 = $29,340
• Total interest: $29,340 - $25,000 = $4,340

When Do You Need to Find the Rate?

There are several common situations where you know the payment but not the rate:

Situation	What You Know	What You Need
Dealer financing	Monthly payment, loan amount, term	Actual rate being charged
Installment plan	Purchase price, monthly payment, number of payments	Effective interest rate
Old loan review	Original amount, current payment, remaining term	Rate you are paying
Comparing offers	Different amounts and payments	Which offer has the lower rate
"0% financing" check	Cash price vs financed price, payments	Whether there is a hidden cost

Spotting Hidden Interest in "0% Financing"

Some retailers advertise "0% financing" but mark up the price compared to the cash price. You can use this calculator to find the effective rate:

Example: A furniture store sells a sofa for $2,000 cash or $90/month for 24 months on "0% financing." Total financed cost: $2,160.

• Enter principal: $2,000, payment: $90, term: 24 months
• Result: 7.4% annual rate
• The "0%" deal actually costs the equivalent of a 7.4% loan because the financed price is $160 higher

Typical Interest Rates by Loan Type

Use this table to check if the rate you find is reasonable for your type of loan:

Loan Type	Typical Rate Range (2025)	Red Flag Above
Mortgage (30-year fixed)	6.0 - 7.5%	8.5%+
Auto loan (new, good credit)	4.5 - 7.0%	10%+
Auto loan (used, fair credit)	8.0 - 14.0%	18%+
Personal loan (good credit)	7.0 - 12.0%	20%+
Student loan (federal)	5.5 - 8.5%	Varies by plan
Credit card (if converted)	18.0 - 28.0%	30%+

If the rate you discover is significantly higher than these ranges, you may be paying more than necessary and should consider refinancing or shopping for a better offer.

Interest Rate vs APR

The rate this calculator finds is the nominal interest rate based purely on the principal, payment, and term. It does not include fees. The APR (Annual Percentage Rate) includes origination fees, closing costs, and other charges, making it higher than the nominal rate. If your loan had upfront fees, the effective APR is higher than the rate shown here. Use the APR calculator to factor in fees.

How Newton's Method Works

Newton's method is an iterative algorithm that refines a guess until it converges on the correct answer. For this calculator:

• Start with an initial guess (e.g., 5% annual rate)
• Calculate what the monthly payment would be at that rate
• Compare it to your actual payment
• Adjust the guess based on how far off it was (using the derivative of the payment formula)
• Repeat until the difference is less than 0.0001%

This typically converges in 5-10 iterations and gives results accurate to at least two decimal places. The same method is used by financial calculators and spreadsheet functions like Excel's RATE().

For the forward calculation (rate to payment), the loan calculator computes monthly payments from a known rate. To see a full payment schedule at the rate you found, use the amortization calculator.

All calculations run in your browser. No data is stored or transmitted.