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Interest Rate Calculator

Find APR · Growth rate · APR ↔ APY

Balances & time
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% Enter balances and time, or loan payments, to solve for the interest rate.

How to Calculate an Interest Rate

An interest rate calculator works backward from known cash amounts and time. Instead of asking how much you will earn at a given rate, you ask which rate produces the outcome you already see on a statement, offer, or investment goal.

Compound growth rate

r = n × ((FV / PV)^(1 / (n × t)) − 1) PV = start · FV = end · n = compounds per year · t = years Example: 10,000 → 15,000 in 5 years, monthly → r ≈ 8.14% APR

Simple interest rate

r = (FV / PV − 1) / t Example: (15,000 / 10,000 − 1) / 5 = 0.10 = 10% per year

Loan APR from payment

P = PMT × (1 − (1 + i)^(−N)) / i Solve for i (periodic rate), then APR = i × payments per year No algebraic shortcut for i; this calculator uses Newton iteration

APR to APY

APY = (1 + APR / n)^n − 1 Continuous: APY = e^APR − 1 · Example: 6% APR monthly → APY ≈ 6.17%
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APY is always at least as large as APR when compounding is more than once per year. They match only for annual compounding.

Reference Table & FAQ

APRAPY (monthly)APY (daily)
3%3.04%3.05%
5%5.12%5.13%
6%6.17%6.18%
8%8.30%8.33%
10%10.47%10.52%
Annual rateApprox years to double
4%18 years
6%12 years
8%9 years
10%7.2 years
12%6 years

Rule of 72 is an approximation. Use Growth Rate mode for an exact required rate.

How do you calculate interest rate from principal and final amount?
Use the compound formula r = n × ((FV / PV)^(1/(n×t)) − 1), or the simple formula r = (FV/PV − 1)/t. Enter start, end, and time in Growth Rate mode to solve it automatically.
What is the difference between APR and APY?
APR is the stated nominal rate. APY includes compounding over a year. Monthly compounding makes a 6% APR equal about 6.17% APY.
How do you find the interest rate on a loan from the payment?
Enter loan amount, payment, and number of payments in Loan APR mode. The tool solves for the periodic rate inside the amortization formula and multiplies by payments per year.

How to Use This Interest Rate Calculator

Growth Rate mode needs a starting balance, ending balance, and time. Choose compound, simple, or continuous interest. Loan APR mode needs principal, payment size, payment count, and how often you pay. APR ↔ APY mode converts a stated rate into an effective yearly yield, or the reverse. Defaults load so you see a solved rate immediately on open.

Read the hero percentage as the solved annual rate. Compare APR and APY in the chips. Use the chart to see how the balance or payment path looks at that rate, and export the detail table when you need numbers for a spreadsheet.

How to calculate the rate manually

1. Identify PV, FV, and years for growth, or P, PMT, and N for a loan. 2. Pick compounding or payment frequency. 3. Apply the matching formula, or iterate on loan rate until the payment equation balances. 4. Convert periodic rate to APR. 5. Convert APR to APY if you need the effective yield.

Worked growth example

$10,000 grows to $15,000 in 5 years with monthly compounding. The ratio is 1.5. Raising 1.5 to the power 1/(12×5) and subtracting 1 gives the monthly rate. Multiply by 12 for the nominal APR of about 8.14%. The matching APY is about 8.45% because monthly compounding adds a little extra effective yield.

If the same balances used simple interest instead, the rate would be (1.5 − 1) / 5 = 10% per year. Compounding lowers the stated APR needed to reach the same ending amount when interest earns interest.

Worked loan example

A $250,000 loan with a $1,800 monthly payment for 360 months implies a specific APR that Loan APR mode solves with Newton iteration. If total payments cannot cover principal even at 0%, the calculator reports that no real non negative rate fits.

Common mistakes

  • Comparing APR from one product to APY from another
  • Using years when the formula expects periods, or the reverse
  • Forgetting that biweekly and semimonthly payment counts differ
  • Assuming simple interest when the account compounds
  • Entering ending balance lower than starting balance for a growth rate (that implies a negative rate)

When this calculator is useful

Use it to reverse engineer a savings rate from two balances, check what APR a quoted loan payment implies, convert bank APR to APY, or estimate the rate needed to hit a future goal. Pair it with the Interest Calculator or Compound Interest Calculator when you already know the rate and want the future balance.

When this calculator may not be enough

It does not price fees into APR the way a Truth in Lending disclosure might, and it does not model irregular payments, balloons, or teaser rates. Credit card interest and daily balance methods need product specific rules.

Limitations

Results are educational math estimates. Loan rate solving assumes level payments and a constant rate. Always confirm rates with the lender or statement before making decisions.

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This tool does not constitute financial advice. Confirm APR, APY, and fees on official disclosures.
What interest rate do I need to double my money?
Set ending amount to twice the start and enter your time horizon in Growth Rate mode. The Rule of 72 gives a quick estimate: years ≈ 72 ÷ annual percent rate. Exact compounding changes the answer slightly.
Is effective interest rate the same as APY?
In consumer savings, APY is the usual label for the effective annual rate after compounding. Finance texts may say EAR or effective interest rate for the same concept.
Can the interest rate be negative?
Yes, if the ending amount is less than the starting amount over positive time, the solved growth rate is negative. That can describe fees, losses, or inflation adjusted declines in purchasing power.

Sources & References