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Interest rate converter

Convert a rate between month, year and day with compound interest, see the gap to simple division, turn an APR into an effective rate and find the true cost of a loan with fees.

Educational simulation. Not investment advice. Results are estimates based on the data you enter and do not replace advice from a qualified professional.

Reviewed on Oct 31, 2026

Equal monthly payments, the first one month after you receive the money. The figure is recalculated from the numbers you enter; your lender’s disclosed APR is the official one.

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Converted rate—
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Compound vs simple interest

Tap the chart to see the values.

Conversion table

Next step

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Method, assumptions and sources

Formulas

Equivalent: i₂ = (1 + i₁)^(n₁ ÷ n₂) − 1, with n = periods per year (year 1, half 2, quarter 4, month 12, day 365, 360 or 252)
Proportional (simple interest): i₂ = i₁ × n₁ ÷ n₂
Effective = (1 + nominal ÷ k)^k − 1; continuous compounding: e^nominal − 1
Monthly true cost: rate i such that amount received = payment × [1 − (1 + i)^−n] ÷ i; annual = (1 + i)¹² − 1

Assumptions and limits

  • True cost computed with equal consecutive monthly payments, the first 30 days after funding; the lender’s disclosed APR uses exact contract dates and may differ slightly.
  • Rates are treated as constant; inflation indexing and taxes on returns are not included.

Official sources and references

Frequently asked questions

How do I convert an annual rate to a monthly rate?

With compound interest, add 1 to the annual rate, raise it to the power 1/12 and subtract 1: (1.07)^(1/12) − 1 = 0.5654% a month. Dividing by 12 (0.5833%) gives the proportional rate, which overstates the true monthly equivalent.

How do I read the result of the page’s example?

The example converts 7% a year to a monthly rate: the equivalent is 0.5654% a month, against 0.5833% by simple division. Over 36 months, $1,000 grows to $1,225.04 with compound interest and $1,210.00 with simple interest at the proportional rate.

What is the difference between APR and APY?

APR is a nominal annual rate: the periodic rate times the number of periods. APY (or effective annual rate) includes compounding. A 24% APR compounded monthly is 2% a month, or a 26.82% APY. Loans usually quote APR; savings usually quote APY.

Why is the true cost of a loan higher than its interest rate?

Because upfront fees reduce the money you actually receive while the payments stay the same. In the page’s loan mode, $10,000 with $300 in fees and 24 payments of $470 gives a contract rate of 0.99% a month but a true cost of 1.24% a month, or 16.0% a year.

When are 252, 360 or 365 days used?

365 calendar days is the most common basis for consumer products. A 360-day year appears in many commercial loan contracts. 252 business days is a convention in some financial markets. Use the basis stated in your contract or account terms.

Where do I find my loan’s rate and fees?

In the loan estimate or disclosure, which should show the interest rate, the APR, the amount financed and the payment schedule. To use this page, enter the loan amount, the fees deducted from what you received, the monthly payment and the number of payments.

Does converting rates settle which loan to choose?

It puts offers on the same basis, which is the first step. Then compare the true cost, the total amount paid and whether the payment fits your budget. For large decisions such as a mortgage, get quotes from several lenders or talk to a financial counselor.

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How to convert interest rates: monthly, annual, APR and true cost

The same rate can be quoted in many ways: monthly, yearly, daily, nominal (APR) or effective (APY). Comparing offers without converting them to the same basis is the fastest way to pick the wrong loan or the wrong savings account.

Annual to monthly (and back)

With compound interest, conversion uses powers: monthly = (1 + annual)^(1/12) − 1 and annual = (1 + monthly)¹² − 1. 7% a year is 0.5654% a month, not 0.5833%. Multiplying or dividing by 12 gives the proportional rate, which only holds for simple interest or for quoting an APR.

Calendar, 360-day and business days

Daily rates depend on the day count: 365 calendar days, a 360-day “banker’s year” used in many loan contracts, or 252 business days used in some markets. The annual rate is the same; what changes is how many days it is spread over.

APR vs APY

A 24% APR compounded monthly means 2% a month, which is 26.82% effective a year. Card and loan rates are usually quoted as APR; savings accounts usually quote APY. Convert both to the effective rate before comparing.

Quoted rateEffective per year
12% compounded annually12.00%
12% compounded monthly12.68%
12% compounded daily12.75%

The true cost of a loan

Fees charged upfront raise the real cost: you repay the same installments after receiving less money. On a $10,000 loan with $300 deducted at closing and 24 payments of $470, the contract rate is about 0.99% a month, but the true cost is about 1.24% a month. U.S. lenders must disclose the APR including certain fees; this page lets you check the math with your own numbers.