# What is my interest rate? Finds the yearly interest rate of a loan from the amount borrowed, the payment and the number of payments, or solves for the payment, the term or the amount. - Page: https://www.acalculator.org/finance/interest-rate-calculator - JSON spec: https://www.acalculator.org/finance/interest-rate-calculator.json - Version: bf80296c5985 ## Default answer Example with the default inputs (Find the Rate, Number of payments 60, Loan amount $20,000.00, Payment $400.00, Balance left at the end $0.00, Payments a year 12, Compounding a year 12, Payments at the End (END)): A $20,000.00 loan repaid with 60 payments of $400.00 has an interest rate of 7.4201% a year. ## Inputs | Key | Label | Description | | --- | --- | --- | | solve | Find the | Which value to work out; type the others. | | n | Number of payments | How many payments there are, for example 60 for five years of monthly payments. | | rate | Interest rate (yearly) | The nominal yearly interest rate in percent, compounded C/Y times a year. | | pv | Loan amount | The amount borrowed. | | pmt | Payment | The payment made each period. | | fv | Balance left at the end | A balloon payment still owed after the last regular payment. 0 for a loan paid off. | | py | Payments a year | How many payments are made in a year: 12 for monthly. | | cy | Compounding a year | How many times a year interest compounds. Usually the same as the payments a year. | | due | Payments at the | The end of each period (usual for loans) or the start of each period (usual for leases). | ## Outputs | Key | Label | Description | | --- | --- | --- | | n | Number of payments | How many payments there are, for example 60 for five years of monthly payments. | | rate | Interest rate (yearly) | The nominal yearly interest rate in percent, compounded C/Y times a year. | | pv | Loan amount | The amount borrowed. | | pmt | Payment | The payment made each period. | | fv | Balance left at the end | A balloon payment still owed after the last regular payment. 0 for a loan paid off. | | periodRate | Rate per period | The interest rate for one payment period, i = (1 + I/Y ÷ C/Y)^(C/Y ÷ P/Y) − 1. | | ear | Effective yearly rate | The rate over a whole year once interest compounds: (1 + i)^(P/Y) − 1. | | totalPmt | Total of payments | The number of payments × the payment. | | interest | Total interest | All the payments plus the balance left at the end, minus the loan amount. | ## Method Loan × (1 + i)^N = payment × (1 + i × t) × ((1 + i)^N − 1) ÷ i + balance left, solved for the rate per period i by search; the yearly rate is 100 × C/Y × ((1 + i)^(P/Y ÷ C/Y) − 1), which is 100 × P/Y × i when compounding matches the payments. ## Assumptions - The interest rate is the same in every period, and every payment is the same size. - The yearly rate is nominal, compounded as many times a year as set; payments are made as many times a year as set. - The loan is money received; the payments and any balance left at the end are money paid. - No fees or taxes are included. This is an estimate for planning, not financial advice. ## Worked examples 1. solve = rate, n = 60, pv = $20,000.00, pmt = $400.00, fv = $0.00, py = 12, cy = 12, due = end gives rate = 7.420096%, totalPmt = $24,000.00, interest = $4,000.00. Source: The loan payment equation of the Texas Instruments BA II PLUS Guidebook (https://education.ti.com/html/eguides/financials/pdfs/EN/BA-II-PLUS_EN.pdf) solved for the rate. 2. solve = rate, n = 48, pv = $8,000.00, pmt = $200.00, fv = $0.00, py = 12, cy = 12, due = end gives rate = 9.241767%. Source: Microsoft Excel RATE function example: 9.24% a year (https://support.microsoft.com/en-us/office/rate-function-9f665657-4a7e-4bb7-a030-83fc59e748ce). 3. solve = pmt, n = 36, rate = 4.75%, pv = $20,000.00, fv = $0.00, py = 12, cy = 12, due = end gives pmt = $597.18, interest = $1,498.32. Source: CFPB, How do I compare auto loan offers? ($20,000 at 4.75% for 36 months: $597 a month, $1,498 interest, https://www.consumerfinance.gov/ask-cfpb/how-do-i-compare-auto-loan-offers-what-should-i-look-at-besides-the-monthly-payment-en-753/). 4. solve = rate, n = 60, pv = $30,000.00, pmt = $450.00, fv = $10,000.00, py = 12, cy = 12, due = end gives rate = 6.754555%. Source: The loan payment equation with a balance left at the end, Broverman (2017), Mathematics of Investment and Credit, chapter 3. ## FAQ ### How do I find the interest rate on a loan? Enter the amount you borrowed, the payment and how many payments there are. A $20,000 loan repaid at $400 a month for 60 months has an interest rate of 7.4201% a year. The rate has no formula of its own, so the calculator tries rates until the payments add up, in today’s money, to exactly the loan. ### Is this rate the same as the APR? It is the rate of the payments you type. When there are no fees, it equals the APR. When the lender charges fees that you pay up front, the APR is higher, because it treats the fees as part of the cost: enter the amount you actually receive (the loan minus the fees) to see that rate. The APR calculator does this for you. ### What is the difference between the interest rate and the effective yearly rate? The interest rate here is a nominal yearly rate: the monthly rate times 12 for monthly payments. The effective yearly rate adds the effect of compounding, (1 + monthly rate)^12 − 1. For the $20,000 example, 7.4201% nominal is 7.6777% effective. ### What if I still owe a balloon payment at the end? Enter the balance left after the last regular payment. A $30,000 loan with 60 payments of $450 and $10,000 still owed at the end has a rate of 6.7546% a year. Leave the balance at 0 for a loan that is fully paid off. ### Why does it say no interest rate fits? The rate must be above −100% and at most 1,000% a year. If the payments add up to less than the loan, the rate would be negative (the calculator shows it, down to −100%); if they are far too high for the loan, the rate would be above 1,000%. Check that the number of payments and the payment are for the same period (monthly payments with the number of months). ### How can I find the payment instead? Choose Payment under Find the, then type the interest rate. $20,000 at 4.75% for 36 months is $597.18 a month, with $1,498.32 of interest in total. ## Sources - Texas Instruments, BA II PLUS Guidebook: the Time-Value-of-Money worksheet and its formulas. https://education.ti.com/html/eguides/financials/pdfs/EN/BA-II-PLUS_EN.pdf - Microsoft, Excel RATE function, with a worked example. https://support.microsoft.com/en-us/office/rate-function-9f665657-4a7e-4bb7-a030-83fc59e748ce - Consumer Financial Protection Bureau, How do I compare auto loan offers? https://www.consumerfinance.gov/ask-cfpb/how-do-i-compare-auto-loan-offers-what-should-i-look-at-besides-the-monthly-payment-en-753/ - S. A. Broverman (2017), Mathematics of Investment and Credit, 7th edition, chapters 2 and 3: annuities and loan repayment.