Interest Rate Calculator
Solve for the rate on a loan or the return on an investment
📐 Loan details
Last updated June 2026
Method: Loan mode solves the standard loan payment equation for the monthly rate by bisection, then reports the nominal APR (rate × 12) and the effective rate (APY). Savings mode uses the compound annual growth rate: (FV / PV)^(1 / years) − 1.
Included: APR, monthly rate and effective annual rate for loans; total interest and total of payments; the CAGR plus total gain and a year-by-year growth table for savings.
Not included: Lender fees, points and other finance charges in the regulatory APR; ongoing deposits or withdrawals; taxes; and irregular payment schedules. Results are estimates, not a loan offer or financial advice.
Interest rate calculator: solve for the unknown rate
Most calculators ask for the interest rate and give you a payment. This one runs in reverse: you already know the numbers, and you want the interest rate hiding inside them. Say a dealer offers you a $25,000 car loan with a $500 monthly payment over 60 months. Multiply it out and you pay $30,000 total - $5,000 of interest - but what rate is that? Working backward from the payment gives roughly 7.42% APR. On the savings side, if you put $10,000 into an account and it grew to $15,000 over 5 years, your money earned about 8.45% per year. This calculator handles both cases.
The loan rate formula
A fixed loan obeys the amortization (present-value of an annuity) equation, which relates the loan amount to the payment, the periodic rate, and the number of payments:
P = PMT × (1 − (1 + r)−n) ÷ r Here P is the loan amount, PMT is the monthly payment, n is the number of monthly payments, and r is the monthly interest rate. The catch: you cannot rearrange this equation to isolate r. Instead the calculator solves it numerically by bisection - narrowing in on the rate that makes the equation balance - then multiplies the monthly rate by 12 to express the result as an annual percentage rate (APR).
The savings (CAGR) formula
When you only have a beginning balance and an ending balance over some years, the single rate that connects them is the compound annual growth rate:
rate = (FV ÷ PV)(1 ÷ years) − 1 where FV is the future (ending) value and PV is the present (starting) value. CAGR smooths out the bumps along the way and tells you the steady yearly rate that would have produced the same end result. It is the standard way to summarize the return on an investment held for several years.
APR vs. effective rate (APY)
APR is the monthly rate times 12 - a nominal figure that ignores compounding. The effective annual rate, or APY, captures monthly compounding with (1 + monthly rate)12 − 1, so it comes out a little higher than the APR. For borrowing, the APY is the true annual cost; for saving, it is the true annual yield. The loan results above show all three so you can see exactly how they line up.
When this is useful
- Hidden financing: a "no interest" furniture or car deal quotes a price and a payment - solve for the rate to see what you are really paying.
- Comparing offers: two loans with the same amount and term but different payments are easy to rank by APR.
- Investment returns: turn "$10k became $15k in 5 years" into a clean annual percentage you can compare to other options, or run the same numbers through the dedicated CAGR Calculator.
- Sanity-checking a quote: confirm the rate a lender stated matches the payment they are charging.
How to use this calculator
You only need three of the four numbers in either mode, and the tool solves for the rate. Work through the fields in order:
- Pick your mode: choose loan if you have a payment and a term, or savings if you have a starting and ending balance over a number of years.
- Loan mode - amount: enter the principal you borrowed (the loan amount), not the sticker price minus any down payment you already paid.
- Loan mode - monthly payment: enter the fixed payment, principal and interest only. Leave out any escrow, insurance or fee add-ons bundled into a single bill.
- Loan mode - number of payments: enter the term in months (a 5-year loan is 60), matching the payment frequency.
- Savings mode - starting and ending amounts: enter the lump sum you began with and the balance you ended with.
- Savings mode - years: enter the whole period the money was invested or saved.
The result updates instantly. Read the headline APR (or CAGR in savings mode) at the top, then check the supporting figures - monthly rate, effective rate, total interest, or year-by-year growth - to see how the rate plays out over the full term.
A second worked example: a personal loan
Suppose you borrow $12,000 as a personal loan and the lender sets a payment of $280 per month for 48 months. Over the full term you pay 48 × $280 = $13,440, so $1,440 is interest. Plugging $12,000, $280 and 48 into loan mode, the calculator solves for a monthly rate of about 0.472%, which it reports as roughly 5.67% APR. The effective annual rate (APY) is a touch higher at about 5.82% because of monthly compounding. Knowing the APR lets you line this offer up against a credit-union quote or a 0% balance-transfer deal on equal footing - the dollar payment alone hides which loan is actually cheaper. If you are weighing several fixed-rate offers, the Personal Loan Calculator turns each rate back into a payment so you can sanity-check both directions.
Who this calculator is for
This tool is built for anyone who has the numbers but not the rate. That includes:
- Car and personal-loan shoppers who want to convert a monthly payment into an APR they can compare across lenders.
- Buyers facing "special financing," where a store quotes a price and a payment but buries the rate in the fine print.
- Investors turning a multi-year gain into a clean annualized return (CAGR) for an apples-to-apples comparison.
- Anyone reviewing an old loan who has the statement figures but cannot find the rate that was originally disclosed.
- Students and the curious who want to see how the amortization equation works backward.
Key terms explained
- Principal: the amount actually borrowed (loan mode) or invested (savings mode). It is the base the rate is applied to.
- Periodic (monthly) rate: the rate charged in a single period. Multiply by 12 for the nominal APR; compound it for the effective rate.
- APR (nominal annual rate): the monthly rate × 12. It ignores compounding and is the figure lenders quote.
- APY / effective annual rate: (1 + monthly rate)12 − 1. It reflects compounding and is the true annual cost or yield.
- CAGR: the constant yearly rate that takes a starting balance to an ending balance over a set number of years.
- Amortization: the structure of a fixed loan in which each level payment covers interest first and the rest reduces principal.
What changes the result the most
If you adjust the inputs and watch the rate move, a few levers dominate:
- Total of payments vs. loan amount (loan mode): the bigger the gap between what you repay and what you borrowed, the higher the implied rate.
- Term length: stretching the same payment over more months lowers the implied rate; a shorter term with the same payment implies a higher rate.
- Ending vs. starting balance (savings mode): a larger ending balance for the same period means a higher CAGR.
- Number of years (savings mode): the same dollar gain spread over more years produces a lower annual rate, because compounding has longer to work.
Limitations and assumptions
This calculator is a planning and comparison tool, not a regulatory disclosure. Keep these assumptions in mind:
- It assumes a fixed payment and a fixed schedule; it does not model variable-rate loans or skipped payments.
- It excludes fees, points and finance charges, so it returns the rate implied purely by the cash flows - not the lender's Regulation Z APR.
- Savings mode assumes a single untouched lump sum; it does not handle ongoing deposits, withdrawals or dividends.
- It does not account for taxes on interest earned or any tax deduction on interest paid, both of which change your effective rate.
- Results are rounded for display; tiny differences from a quoted figure are usually fees or compounding conventions, not errors.
Why credit cards are different
People often arrive here wanting the interest rate on a credit card, but a card does not fit the loan equation cleanly. A fixed installment loan has three locked numbers - the amount borrowed, a level payment, and a set number of payments - so there is exactly one rate that ties them together. A credit card is revolving: the balance changes every month as you spend and pay, and you are only required to make a small minimum, so there is no fixed term n to solve against. That is why this calculator does not try to back out a card's rate from a payment. The good news is you never have to: a card's purchase APR is disclosed on every statement and in the cardholder agreement, so you can read it directly. To see how long a balance takes to clear at that rate - and how much interest it costs - feed the balance and APR into the Credit Card Payoff Calculator or the broader Debt Payoff Calculator instead.
Zero, negative, and "too good to be true" rates
Edge cases tell you a lot about what the math is really doing. A 0% rate in loan mode is legitimate and simply means your payment times the term equals the loan amount exactly - genuine 0% promotional financing works this way, with no interest at all. A result the calculator rejects is a negative loan rate: if your payments add up to less than you borrowed, no positive rate fits, and rather than print a nonsense figure the tool flags it so you can recheck the inputs. In savings mode the rules flip. A negative CAGR is perfectly valid and just means the ending balance came in below the starting balance - you lost money over the period, and the annualized loss is useful information. And if a "guaranteed" return looks implausibly high once you annualize it, that is exactly the kind of red flag the rate math is meant to surface: convert any pitch into a clean annual percentage before you compare it to a safe benchmark like a high-yield savings account or a CD on the CD Calculator.
How it compares to related calculators
This page answers "what rate is hiding in my numbers?" If your question is different, a sister tool fits better:
- To turn a known rate into a monthly loan payment, use the Loan Calculator.
- To compare the true cost of loans including fees, use the APR Calculator.
- To project how savings grow with regular contributions, use the Compound Interest Calculator.
- To convert a nominal rate into a true annual yield, use the APY Calculator.
- To work out the annualized return on an investment on its own, use the CAGR Calculator.
- To convert a payment into the rate on a vehicle deal, use the Auto Loan Calculator or check a fixed-rate offer with the Personal Loan Calculator.
Sources
- Consumer Financial Protection Bureau (CFPB) - Interest rate vs. APR.
- Consumer Financial Protection Bureau (CFPB) - What is a finance charge?
- Truth in Lending Act (Regulation Z) - federal rules defining how the APR on a consumer loan is calculated and disclosed.
⚠️ Common mistakes & edge cases
Confusing APR with the regulatory APR
This tool solves for the rate implied by your loan amount, payment and term only. A lender's disclosed APR also bakes in fees and points, so it can be noticeably higher. They answer different questions - don't expect them to match to the decimal.
Mixing up months and years
The loan term must be in the same units as the payment. A 5-year loan is 60 monthly payments, not 5. Entering "5" for a monthly-payment loan will report a wildly wrong rate.
Payments that total less than the loan
If your payment times the term is below the loan amount, there is no positive interest rate - you would be repaying less than you borrowed. The calculator flags this rather than returning a meaningless negative rate.
Using CAGR when you added money along the way
The savings mode assumes a single untouched lump sum. If you made monthly contributions, the single CAGR won't describe each deposit accurately - use a compound interest calculator with contributions instead.
❓ Frequently asked questions
How do you find the interest rate on a loan?
There is no simple closed-form formula to solve for the rate, so this calculator uses bisection: it repeatedly tries monthly rates in the loan payment equation P = PMT x (1 - (1 + r)^-n) / r until the implied payment matches yours. The monthly rate is then multiplied by 12 to report the nominal APR. You need three of the four values - loan amount, monthly payment, and number of payments - to solve for the fourth (the rate).
How do you calculate the interest rate on savings or an investment?
If you know only a starting amount and an ending amount over a number of years, the constant annual rate is rate = (FV / PV)^(1 / years) - 1, where FV is the future (ending) value and PV is the present (starting) value. This is the compound annual growth rate, or CAGR. For example, $10,000 growing to $15,000 in 5 years is (15000/10000)^(1/5) - 1 = 8.45% per year.
What is the difference between the monthly rate, APR and APY?
The monthly rate is the periodic rate charged each month. The APR (annual percentage rate) is simply the monthly rate multiplied by 12 - a nominal figure that ignores compounding. The APY or effective annual rate accounts for monthly compounding: (1 + monthly rate)^12 - 1, so it is slightly higher than the APR. Lenders quote APR; the APY shows the true compounded cost or yield.
Why does my result differ from the rate my lender quoted?
A lender's APR is defined by Regulation Z and folds in finance charges such as origination fees, points and certain closing costs, then spreads them across the payments. This calculator solves for the rate implied purely by your loan amount, payment and term. If there were fees rolled into the loan, the regulatory APR will be higher than the pure payment-based rate shown here.
Can I use this to compare two loan offers?
Yes. Enter the loan amount, the monthly payment and the number of months for each offer and compare the resulting APRs. The lower APR is cheaper for the same loan amount and term. Just remember that fees a lender bundles into the loan are not captured unless they are already reflected in the amount you finance.
Does the savings mode account for deposits or withdrawals?
No. The savings (CAGR) mode assumes a single lump sum that grows untouched from the starting amount to the ending amount. If you make regular contributions, the single annual rate it reports will not describe each individual deposit - use a compound interest calculator with contributions for that scenario.
What if the payments add up to less than the loan amount?
Then there is no positive interest rate that fits, because you would be repaying less than you borrowed. The calculator flags this. Check that the monthly payment and term are correct - together they must total more than the loan amount for interest to exist.
What is a good interest rate?
It depends entirely on the product and the market at the time. For loans, lower is always better for you; a 'good' auto or personal loan rate is one near the bottom of the range lenders offer for your credit tier, which is why shopping several lenders matters. For savings and investments, higher is better, but compare against safe benchmarks like high-yield savings, CDs, or Treasury yields. This calculator does not judge whether a rate is good - it simply tells you the rate implied by your numbers so you can compare it against current offers yourself.
Does this calculator work for credit cards?
Loan mode works best for fixed installment loans with a set payment and term, like a car loan or personal loan. Credit cards use revolving balances and only a minimum payment, so there is no fixed n to solve against. If you want the rate on a card, read the APR directly from your statement - it is disclosed there - and use a credit card payoff calculator to see how long a given payment will take.
How accurate is the bisection method?
Very accurate for practical purposes. Bisection repeatedly halves the search range, so each step roughly doubles the precision; after enough iterations the implied payment matches your entered payment to a fraction of a cent. The reported APR is reliable to two decimal places. Any difference you see from a lender's figure comes from fees folded into their regulatory APR, not from rounding in the math.
Can the interest rate be zero or negative?
A true 0% loan is possible - it means your payments times the term exactly equal the loan amount, with no interest at all. Genuine 0% promotional financing works this way. A negative rate would mean you repay less than you borrowed, which the calculator treats as an error in loan mode. In savings mode, a negative CAGR is valid and simply means the ending balance is lower than the starting balance, i.e. you lost money over the period.
💡 Good to know
The payment hides the rate on purpose
"$0 down, just $299/month" sounds simple, but the rate is buried in the relationship between the amount, the payment and the term. Solving for it is the only way to compare a dealer or store offer against a plain bank loan on equal terms.
A lender's APR will usually be higher than this
This tool finds the rate implied by your cash flows alone. The APR a lender must disclose under the Truth in Lending Act also folds in origination fees and points, so it is the better number for shopping - expect it to sit a bit above the figure here.
CAGR smooths out a bumpy ride
An investment that zig-zags up and down can still be summarized by one annual rate. CAGR ignores the path and reports the steady yearly growth that would have reached the same ending balance - handy for comparing very different investments.