Interest Rate Calculator

What this calculator does that the other Lelifi interest tools do not

Several interest tools already live on this site, and each one owns a different question. The simple interest calculator prices a flat charge on a principal with no compounding. The compound interest calculator grows a balance across compounding periods. The effective interest rate calculator turns a quoted nominal rate into the effective annual rate. The APR calculator starts from a rate the lender quotes, adds the fees, and reports the APR. This page runs the opposite direction. You start with the three numbers a lender puts in front of you, the amount, the term and the monthly payment, and you solve backward for the rate that payment implies. Then you fold points and fees into that rate and line up two quotes side by side.

Payment shopping feels safer than rate shopping, because a payment is a number you can imagine paying every month. But a payment hides the rate, and the rate hides the fees. A quote can carry a payment that looks easy and still be the more expensive loan.

Solving a rate backward from a payment

Lenders price a loan forward. Given a principal P, a monthly rate i and a number of months n, the payment comes from the standard annuity relation: payment = P x i / (1 - (1 + i) raised to the power of negative n). Running that backward is different. No simple algebra isolates i, so a solver guesses a rate, computes the payment, and compares it with yours. If the computed payment is too high, the solver steps down; if too low, it steps up. Within a few dozen rounds the rate is solved.

Worked example. Take a $15,000 loan over 48 months with a payment of $366.19. The solved rate is 8.00% a year, which is 8 / 12 = 0.67% a month. Check it by running the loan forward: 366.19 x 48 = 17,577.12 in total payments, and 17,577.12 - 15,000 = 2,577.12 of interest over four years. A payment of $355.72 on the same amount and term solves to 6.50%, a point and a half cheaper. Both payments look comfortable side by side. Only one of them is free of fees.

Two details matter before you trust a solved rate. Enter principal and interest only, because a payment that includes escrow for taxes or insurance reads as extra interest. And expect rounding, since lenders quote payments to the cent, so a result of 7.9995% against an advertised 8.00% is normal.

Points and fees: the rate on the cash you receive

A point is an upfront fee of 1% of the loan amount, paid at closing. The Consumer Financial Protection Bureau explains that points let you trade upfront cash for a lower rate, and that one point on a $100,000 loan equals $1,000. Its explainer on points and lender credits also notes that some lenders use the word points for any percentage based fee, whether or not a rate reduction comes with it, so read the line items rather than the label. Origination fees are usually flat dollars, and a broker fee can show up as points, a flat fee, or an addition to the rate.

Here is where the rate changes meaning. The lender sets the payment from the full amount and the stated rate, but you never receive the full amount, because points and fees leave before the money reaches your account. So the honest rate is the one that makes those same payments equal the smaller amount that landed in your account. Take the $15,000 example again with 2 points and a $300 origination fee: the fee dollars are 300 + 300 = 600, the cash you receive is 15,000 - 300 - 300 = 14,400, and the same $366.19 payment against $14,400 solves to an all-in rate of 10.14% instead of 8.00%.

Fees bite harder on short loans. The same $600 spread over 48 payments lands on more of your money per payment than it would over 72 payments, which is why a two year personal loan and a seven year mortgage can carry a different fee load for the same dollars borrowed.

Each point here costs $150 and lifts the all-in rate by about half a point.

Quote A versus quote B: when the lower payment loses

Now put two real quotes side by side. Both are for $15,000 over 48 months. Quote A has the smaller payment and the lower stated rate, plus 3 points and a $600 fee. Quote B has the larger payment, a higher stated rate, and no fees. On paper quote A looks like the winner on every line a borrower normally checks.

Do the arithmetic. Quote A collects 355.72 x 48 = 17,074.56 and adds 1,050 of upfront charges for 18,124.56 all in. Quote B collects 366.19 x 48 = 17,577.12 with nothing else to add. The gap is 18,124.56 - 17,577.12 = 547.44. The quote with the smaller monthly bill costs more, and the all-in rate says why: 10.28% against 8.00%.

Quote A saves 366.19 - 355.72 = 10.47 a month, so the $1,050 in upfront charges takes 1,050 / 10.47 = 100.29 months to earn back. Since the loan lasts 48 months, the points never pay off and quote A is the worse deal.

What APR means under Regulation Z

The annual percentage rate is the number the law uses to make loans comparable. The Truth in Lending Act put the rule in place, and the Consumer Financial Protection Bureau writes the details in Regulation Z. Section 1026.22 of Regulation Z says the APR is a measure of the cost of credit expressed as a yearly rate that relates the amount and timing of the value the consumer receives to the amount and timing of the payments made, and the regulation spells out an actuarial method with the equations and examples in appendix J.

Two practical details from that section are worth keeping. For a regular transaction, a disclosed APR counts as accurate when it is no more than 1/8 of 1 percentage point above or below the exact rate, which is the tolerance most lenders round to. And a mortgage APR is not identical to a credit card APR, because the fees that must be counted differ, so the two numbers cannot be compared with each other.

The CFPB page on mortgage rates and APRs explains that the interest rate is what you pay to borrow the money without fees, while APR reflects points, broker fees and other charges. The Federal Trade Commission's mortgage shopping guide adds that knowing only the payment or the rate is not enough, and that APR is what makes two offers comparable.

One distinction to keep straight. The rate this calculator solves is a nominal yearly rate, the monthly rate times 12, because that is how a lender quotes a closed end loan. The effective annual rate includes the effect of compounding inside the year, and the Lelifi effective interest rate calculator handles that conversion.

Reading two loan quotes like a careful shopper

A good comparison takes five numbers from each quote, and every one has to match up. They are the amount borrowed, the term in months, the monthly payment for principal and interest, the number of points, and every flat fee on page one of the Loan Estimate. With those in hand, run each quote through this page and read the all-in rate row for both.

Then ask two questions. Is the all-in rate the lower one, and if the two rates land close together, is the total cost the lower one. And will you keep the loan long enough to earn the points back. The break-even test is a division: the points and fees you pay upfront divided by the monthly payment the points save. If that number is longer than the term, the points are a cost with no payoff.

The CFPB report on discount points notes that borrowers benefit only if they keep the loan past the break-even period, and that the rate drop per point varies by lender.

Two habits protect you here. Ask every lender for the Loan Estimate in writing, so you compare the same fee lines instead of a conversation with a document. And when a quote comes back with points, ask what the rate would be with zero points, since a CFPB explainer notes that a one point loan should carry a lower rate than a zero point loan from the same lender.

How to use this calculator

Enter quote A in the first block and quote B in the second. For each one you need the amount, the term, the payment, the points and the upfront fees. Leave the points and fee boxes at zero for a loan with no upfront charges, and the results fill in as you type. The rows show the rate implied by the payment, the cash you receive after fees, the all-in rate, the total of payments, the total interest and the all-in cost, which adds fees to payments.

The verdict line under the table tells you which quote has the lower all-in rate and which costs less overall. If the two rates are close, the tiebreaker is the all-in cost and how much cash you need at signing, since a quote with fees can ask for far more money on day one for the same monthly number.

Take one extra step before you rely on the answer. Compare the all-in rate with the APR the lender printed on the disclosure. If the lender says 8.00% and your solved rate comes back as 8.00%, you read the paperwork the way the lender read it. If the numbers are far apart, the usual reason is a payment that includes escrow or insurance, so pull that out and solve again. Everything here runs in your browser, and nothing you type is uploaded or stored.