APR / APY Calculator
One rate can be quoted three different ways. This tool converts a rate you already know into the form that lets you compare offers: nominal into effective yield for savings, and nominal into cost-inclusive APR for loans.
APY folds compounding into the rate, so two savings offers quoted at the same nominal rate but compounded differently can be compared side by side.
Add a balance to see the APY as a dollar figure: Interest = Principal x (APY/100).
Your converted rate will appear here
Pick APY for a savings offer or APR for a loan, fill in what you know, then calculate.
Which of our tools do you actually need?
APR/APY vs. our Interest Rate Calculator: that tool solves for an unknown rate out of a borrowing or saving scenario. This page converts a rate you already know between forms: nominal into effective (APY), and nominal into cost-inclusive (APR).
APR/APY vs. our Compound Interest Calculator: that one gives you a closing balance and the growth on the way there. APY gives no closing balance at all. It is a yardstick for comparing offers that compound at different frequencies. Rule of thumb: APY answers which offer is better?, compound interest answers how much will I have?
Also worth a look: the Loan Calculator and Mortgage Calculator give you the monthly payment. The APR side of this page gives you the total price of the borrowing, fees and points included.
Quick Answer
APY = (1 + r/n)^n - 1, where r is the nominal annual rate and n is the number of compounding periods per year. A 6% nominal rate compounded monthly works out to an APY of 6.17%. On the borrowing side, APR takes the interest rate and adds points, broker fees and other charges, which is why a lender's APR usually sits above the interest rate printed next to it.
How It Works: Formula & Variables
APY from a nominal rate
APY = (1 + r/n)n − 1
- r
- The nominal annual rate as a decimal. A 6% rate is 0.06.
- n
- Compounding periods per year: 1 annually, 2 semiannually, 4 quarterly, 12 monthly, 365 daily.
US banking regulation writes the same thing with a percentage output: APY = 100 × [(1 + i/n)n − 1]. The two are identical, one just multiplies by 100 for you.
APY from interest you already earned
APY = 100 × [(1 + Interest/Principal)(365/Days in term) − 1]
Running it the other way, if you know the APY and the balance: Interest = Principal × (APY/100).
What APR includes that the interest rate does not
The Consumer Financial Protection Bureau puts it plainly. The interest rate is “the cost you will pay each year to borrow the money... It does not reflect fees or any other charges.” An APR, by contrast, is “a broader measure of the cost of borrowing money than the interest rate. The APR reflects the interest rate, any points, mortgage broker fees, and other charges that you pay to get the loan. For that reason, your APR is usually higher than your interest rate.”
On points: “One point equals one percent of the loan amount. For example, one point on a $100,000 loan is one percent of the loan amount, which equals $1,000.”
How exact does a quoted APR have to be?
US rules give lenders a small allowance. A disclosed APR is treated as accurate when it falls within 1/8 of a percentage point of the APR calculated under the regulation. For an irregular transaction, meaning one with multiple advances or irregular payment periods or amounts, the allowance widens to 1/4 of a percentage point. So a lender quoting 6.50% and a calculator saying 6.53% are not in disagreement.
Worked Examples
Example 1: a 6% nominal rate compounded monthly
Take a nominal APR of 6% with monthly compounding, so n = 12. APY = (1 + 0.06/12)12 − 1 = 1.00512 − 1 = 0.06167781186, which is 6.17%. The extra 0.17 of a point is the compounding showing up.
Frequency matters less than people expect. On $10,000 for a year at a 5% nominal rate, semiannual compounding gives an APY of 5.0625% and $506.25 of interest. Monthly compounding gives 5.1164% and $511.62. The gap is about five dollars.
Example 2: a $3 fee turns a 10% rate into a 25% APR
Borrow $20 for one year at 10% interest with a $3 fee. At the end you owe 20 + (20 × 10%) + 3 = $25. Five dollars of that is cost, and 5/20 = 0.25, so the APR is 25% while the interest rate is still 10%.
Drop the fee and the picture changes completely: 20 + 2 = $22 owed, 2/20 = 0.10, and the APR is 10%, identical to the interest rate. Fees are the entire reason the two numbers ever differ.
Key Concepts
Nominal, effective, cost-inclusive: one rate, three ways of writing it. Nominal is the headline figure. Effective (APY) adds compounding. Cost-inclusive (APR) adds fees and points.
APY is a comparison tool, not a projection: it tells you which of two savings offers pays more per dollar, and stops there. For a closing balance, run the numbers through a compound interest projection instead.
Fees move the APR far more than compounding moves the APY: a few thousand dollars of closing costs can add half a point to a mortgage APR. Switching from annual to daily compounding on a savings account moves the APY by hundredths.
Not every fee counts: some charges are not treated as finance charges and stay out of the APR calculation. Ask your lender which of your costs actually belong in the number.
Common Mistakes
Treating APR and the interest rate as the same number: they only match when there are no fees or points at all. Comparing one lender's rate against another lender's APR will mislead you every time.
Assuming every fee is a finance charge: CalculatorSoup warns about this directly, noting that “Some fees are not considered 'financing charges' so you should check with your lending institution”. Throwing all your closing costs into the box inflates the APR.
Chasing compounding frequency: the jump from annual to daily compounding is worth a few basis points. Finding a bank paying half a point more is worth far more than that, and takes about the same effort.
Frequently Asked Questions
The nominal APR is the base rate with no compounding built into it, while APY takes compounding into account. On the borrowing side the APR is also broader than the interest rate itself, because it includes the rate, points, mortgage broker fees and other charges you pay to get the loan.
Because the APR counts points and fees on top of the interest. Strip those out and the two figures land in the same place. Borrowing $20 for a year at 10% costs $2 in interest, so both the rate and the APR come to 10%. Add a $3 fee and $5 of the $20 is now cost, which is an APR of 25% against the same 10% rate.
One point equals one percent of the loan amount. One point on a $100,000 loan is one percent of the loan amount, which equals $1,000. Points do not have to be round numbers, so half a point or 1.375 points are both normal.
In the US, a disclosed APR counts as accurate if it sits within 1/8 of a percentage point of the APR calculated under the rules. For an irregular transaction, meaning multiple advances or irregular payment periods or amounts, the allowance widens to 1/4 of a percentage point.
Yes, but only slightly. At a 5% nominal rate, semiannual compounding gives an APY of 5.0625% and monthly compounding gives 5.1164%. On $10,000 that is $506.25 against $511.62, so about five dollars separates them over a year.
Yes. Use APY = 100 x [(1 + Interest/Principal)^(365/Days in term) - 1]. Earning $50 on $1,000 across 365 days gives an APY of 5%.
Related Calculators
Compound Interest Calculator
Project a balance forward and compare annual, monthly, daily and continuous compounding.
Interest Rate Calculator
Solve for an unknown rate when you know the starting and ending amounts.
CD / Money Market Calculator
Run a fixed-term deposit with penalties, tax handling and a yield-to-term column.
Loan Calculator
Monthly payment, total interest and payoff time on any fixed-rate loan.
Mortgage Calculator
Monthly mortgage payment including taxes, insurance, PMI and HOA fees.
Amortization Calculator
The full payment-by-payment schedule behind a fixed-rate loan.
Sources
- TheCalculatorSite, APY Calculator (APY formula, derived formulas, compounding-frequency comparison): https://www.thecalculatorsite.com/finance/calculators/apy-calculator.php
- 12 CFR Part 1030, Appendix A (Truth in Savings, Regulation DD; statutory APY formula): https://www.ecfr.gov/current/title-12/chapter-X/part-1030/appendix-Appendix A to Part 1030
- Consumer Financial Protection Bureau, mortgage interest rate vs. APR: https://www.consumerfinance.gov/ask-cfpb/what-is-the-difference-between-a-mortgage-interest-rate-and-an-apr-en-135/
- Consumer Financial Protection Bureau, discount points and lender credits: https://www.consumerfinance.gov/ask-cfpb/what-are-discount-points-and-lender-credits-and-how-do-they-work-en-136/
- 12 CFR 1026.22 (APR accuracy tolerances): https://www.law.cornell.edu/cfr/text/12/1026.22
- CalculatorSoup, APR Calculator (the $20 loan example and the finance-charge caveat): https://www.calculatorsoup.com/calculators/financial/apr-calculator.php