Interest Rate Calculator
Work backwards from a loan amount, a monthly payment and a term to the interest rate you are actually being charged — and see how that differs from APR.
Interest Rate Calculator: with the default inputs, interest rate is 7.42%.
What you actually received, or the cash price of the item financed.
The level payment the contract requires.
Nominal annual rate — the monthly rate × 12, which is how lenders quote it.
- Monthly rate
- 0.6183%
- Effective annual rate
- 7.678%What the monthly compounding is really worth over a year.
- Total of payments
- $30,000.00
- Total interest
- $5,000.00
- Interest as a share of the amount
- 20%
- Number of payments
- 60
Assumptions
- Level monthly payments with interest compounded monthly on the declining balance.
- The nominal annual rate is the monthly rate × 12, the US convention.
- No fees are added; the rate found is the rate implied by the amount you entered.
| Month | Payment | Principal | Interest | Balance |
|---|---|---|---|---|
| 1 | $500.00 | $345.41 | $154.59 | $24,654.59 |
| 2 | $500.00 | $347.55 | $152.45 | $24,307.03 |
| 3 | $500.00 | $349.70 | $150.30 | $23,957.34 |
| 4 | $500.00 | $351.86 | $148.14 | $23,605.47 |
| 5 | $500.00 | $354.04 | $145.96 | $23,251.44 |
| 6 | $500.00 | $356.23 | $143.77 | $22,895.21 |
| 7 | $500.00 | $358.43 | $141.57 | $22,536.78 |
| 8 | $500.00 | $360.65 | $139.35 | $22,176.13 |
| 9 | $500.00 | $362.88 | $137.12 | $21,813.26 |
| 10 | $500.00 | $365.12 | $134.88 | $21,448.14 |
| 11 | $500.00 | $367.38 | $132.62 | $21,080.76 |
| 12 | $500.00 | $369.65 | $130.35 | $20,711.11 |
How this is worked out
The formula
Solve for i in PMT = P × i(1 + i)^n ÷ ((1 + i)^n − 1) P = amount borrowed PMT = monthly payment n = number of monthly payments The payment rises monotonically with i, so the rate is found by bisection. Nominal annual rate = i × 12. Effective annual rate = (1 + i)^12 − 1.
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- Amount borrowed
- What you actually received, or the cash price of the item financed.in dollars · 0 or more · defaults to 25000
- Monthly payment
- The level payment the contract requires.in dollars · 0 or more · defaults to 500
- Term — years
- A number.from 0 to 50 · whole numbers only · defaults to 5
- Term — extra months(under More options)
- A number.from 0 to 11 · whole numbers only · defaults to 0
What you get back
- Interest ratemain answer
- Nominal annual rate — the monthly rate × 12, which is how lenders quote it.
- Monthly rate
- Effective annual rate
- What the monthly compounding is really worth over a year.
- Total of payments
- Total interest
- Interest as a share of the amount
- Number of payments
What this assumes
- Level monthly payments with interest compounded monthly on the declining balance.
- The nominal annual rate is the monthly rate × 12, the US convention.
- No fees are added; the rate found is the rate implied by the amount you entered.
About this calculator
Some offers never mention a rate. A furniture store quotes "$149 a month for 36 months", a dealer advertises a payment, a rent-to-own contract lists a weekly figure. Give this calculator the amount, the payment and the term, and it inverts the amortization formula to find the rate hiding inside.
How to use it
Enter the amount you actually receive — the cash price of the item, or the money deposited in your account — then the contractual payment and the term. If the payments don't add up to at least the amount borrowed, no rate exists and the calculator says so rather than returning nonsense.
Nominal, effective and APR are three different numbers
- The interest rate shown here is the nominal annual rate: the monthly rate times 12. This is how US lenders quote loans, and it's the rate that generates the payment.
- The effective annual rate compounds that monthly rate through a year. 7.42% nominal is 7.68% effective. It's the number to use when comparing against an investment return or an APY.
- APR is a legal construct, defined by Regulation Z. It folds prepaid finance charges — origination fees, points, mortgage insurance, some closing costs — into the rate, so a loan with fees has an APR above its note rate. If the amount you enter here is the cash you received net of fees, the answer you get is the APR. If it's the gross amount before fees came out, the answer is the note rate and the true APR is higher.
That last distinction is the whole trick to reading a loan offer. A lender who charges a 5% origination fee on a $15,000 loan at 11.5% is really charging about 13.8%: enter $14,250 (what hit your account) rather than $15,000 and you'll see it.
What the rate does not tell you
A rate is not a cost. A 24% rate on a $500 loan for three months costs $23; a 6% rate on $400,000 for 30 years costs $463,000. Look at the total interest line as well, and remember that the term is usually the bigger lever: stretching a car loan from 48 to 84 months at the same rate roughly doubles the interest.
Caveats
The model assumes level monthly payments, monthly compounding, and no fees beyond whatever you excluded from the amount. Loans with irregular payments, a balloon, or interest computed by the Rule of 78s will not match. For those, use the finance calculator with a balloon in FV, or the APR calculator with the fee schedule.
Frequently asked questions
▸Is the rate this gives me the APR?
Only if the amount you entered is the net cash you received after fees. APR under Regulation Z includes prepaid finance charges, so enter the loan proceeds rather than the face amount and the answer becomes the APR.
▸Why is the effective rate higher than the quoted rate?
Because interest compounds monthly. A 7.42% nominal rate charged as 0.6183% a month works out to 7.68% over a full year. Lenders quote the nominal figure; savings accounts quote the effective one (APY), which is why the two never look comparable.
▸What if the payments total less than I borrowed?
Then there is no positive interest rate — either the term or the payment is wrong, or part of the balance is forgiven or due as a balloon. The calculator returns an error instead of a negative rate.
▸Does this work for a mortgage?
Yes, for principal and interest. Exclude escrow items — taxes, insurance and HOA are not interest and will inflate the answer badly if you leave them in the payment.
▸How do I find the rate when there's a balloon payment?
Use the finance calculator: put the amount in PV, the payment in PMT, the balloon in FV, and solve for the rate.
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