APR vs APY Calculator

• Converts an APR to an APY, or an APY back to its APR, for annual, semiannual, quarterly, monthly, daily or continuous compounding.
• Tabulates the effective rate at every compounding frequency so you can see how little the frequency matters past monthly.
• Finds a loan's APR including upfront fees and points, and shows how the rate climbs if you repay early.
• Compares two savings or loan offers on a like-for-like effective rate, with dollars per year and a side-by-side grid.

How to use this calculator

Choose what you want to do. Convert takes a rate, tells the calculator whether it is an APR or an APY, picks how often interest compounds, and returns the other figure along with dollars of interest on an amount you choose. Find a loan's APR with fees takes the amount, term, rate and upfront fees and returns the APR once fees are counted. Compare two offers converts both to a common effective rate and declares a winner.

For the comparison, enter offer A in the main fields and offer B under Advanced. Choose whether the offers are for savings, where a higher rate wins, or a loan, where a lower cost wins. For loans, each offer can have its own upfront fees, so the comparison reflects the full cost.

This tool is about the rate. To see how a savings balance grows with regular deposits, use the High-Yield Savings and APY Calculator.

APR versus APY

APR, the annual percentage rate, is a yearly rate stated before compounding. APY, the annual percentage yield, is the rate you actually earn or pay over a year once compounding is counted. If interest is added to your balance more than once a year, each addition earns interest too, so the APY is higher than the APR.

APY = (1 + APR/m)^m - 1          m = compounding periods a year
APR = m x ((1 + APY)^(1/m) - 1)
Continuous compounding: APY = e^APR - 1 ,  APR = ln(1 + APY)

A 6% APR compounded monthly means 0.5% is added each month. After twelve months the balance has grown by (1.005)^12 minus 1, which is 6.168%. On $20,000 that is $1,233.56 of interest, against $1,200 if the 6% were paid once at year end. Going the other way, a savings account advertising 5.00% APY pays an APR of 4.889% compounded monthly.

The two measures are used differently. Banks advertise savings by APY, which looks larger, as required for deposit accounts under the Truth in Savings rules. Lenders quote loans by APR, which looks smaller. Compare savings by APY and loans by APR, and convert before comparing across the two.

Credit cards illustrate the gap well. A card advertising 24% APR charges interest daily on the balance, so a customer who carries the debt for a full year pays more than 24% of the average balance. The card issuer is required to disclose the APR, not the higher effective rate, which is why running the conversion yourself shows the real annual cost of carrying a balance. The same arithmetic explains why a small positive savings rate can look larger as an APY: the more often interest is added, the more the two numbers diverge.

How much does compounding frequency matter?

Less than people expect. For the same 6% APR, the effective rate is 6.000% compounded annually, 6.090% semiannually, 6.136% quarterly, 6.168% monthly, 6.183% daily and 6.184% continuously. The jump from annual to monthly is 0.168%; from monthly to daily it is only 0.015%; from daily to continuous, 0.0005%.

Continuous compounding is the mathematical limit as the period shrinks to nothing. No bank adds interest at every instant, but daily compounding comes extremely close, so the continuous figure is a useful ceiling. At higher rates the differences grow. At a 20% APR compounded monthly the APY is 21.94%, which is why credit card rates quoted as APRs understate the real annual cost for anyone carrying a balance.

The rate number matters far more than the frequency. A 0.25 percentage point higher APR is worth more than switching from monthly to daily compounding on any ordinary savings rate.

A loan's true APR with fees

The stated rate on a loan is not always what it costs. If you pay an origination fee or points at closing, you receive less than the loan amount but repay all of it with interest. The APR disclosed to borrowers captures this by finding the rate that makes the payments worth exactly the amount you received:

Amount received = Sum of payment / (1 + x)^t     for t = 1 to n
APR including fees = 12 x x   (x = monthly rate that solves the equation)

Take a $20,000 loan at 6.00% over 60 months with $600 of upfront fees. The payment is $386.66, but you receive $19,400. The APR including fees is 7.274%, which is 1.27% above the stated rate. Without fees it is exactly 6.000%. Over a longer term the fee is spread thinner: at 84 months the APR is 6.934%.

Fees weigh most when you repay early, because you pay them in full whatever the loan's length. The same loan repaid after 12 months has a true APR of 9.43%, after 24 months 7.95% and after 36 months 7.50%. The calculator tabulates this. The effective annual rate it also shows is the APR with monthly compounding counted, 7.521%, which is the figure to compare against a savings yield.

Federal rules require lenders to disclose an APR that includes certain prepaid finance charges, and allow a small tolerance (one-eighth of a percentage point on regular loans). Which fees count depends on the type of loan, so ask for every fee in writing and enter the ones that apply.

Comparing two offers quoted differently

The real use of APY and APR is putting two offers on the same footing. Say a savings account offers 6.00% APR compounded monthly and another advertises 6.10% APY. The first looks lower, but its APY is 6.168%. The second is 6.100%, so the first is ahead by 0.068% a year, about $14 on $20,000 and $86 after five years.

For loans, the same offers work in reverse and fees matter. If the 6.00% loan charges $600 up front and the other charges none, the effective rate with fees is 7.521% for A against 6.100% for B, so B wins by a wide margin. The total cost of borrowing is $636 less. A lower stated rate with a large fee will often lose to a slightly higher rate with none, especially on a short loan.

The side-by-side grid highlights the better offer in each row. Offers are treated as fixed for the whole period. Variable rates, introductory rates and balance-tiered savings rates need a separate comparison for each period.

Check the conditions behind a headline savings rate before you rely on it. Some accounts pay the top rate only on a limited balance, for a promotional period, or if you meet monthly activity requirements. A rate that applies to only part of your money is worth less than its APY suggests, so compare what you would actually earn on the amount you plan to deposit. For certificates of deposit the APY already assumes you leave the interest in the account for the full term, and an early withdrawal penalty can reduce the effective return.

For loans, check whether the quoted rate is fixed and whether you can repay early without a penalty. A prepayment charge turns the early-payoff table above into a worse picture, because it is a cost on top of the fees already counted. If you might sell or refinance within a few years, the APR over that shorter horizon is the number to compare.

Assumptions and limitations

• Fixed rates. Savings and loan rates are assumed constant. Many savings rates can change at any time.
• Monthly loan payments. Loan results assume equal monthly payments. The compounding setting controls how the quoted rate accrues, and it is converted to an equivalent monthly rate.
• 365-day year. Daily compounding uses 365 days, as in the federal APY formula for deposit accounts. Loans that accrue interest on a 360-day year are not modelled and can cost slightly more than shown.
• Fees are prepaid. Fees you enter are deducted from the amount you receive. Fees paid later, insurance and taxes are not included.
• Dollar figures are illustrative. They assume one deposit or loan amount and no further deposits or withdrawals.
• No tax. Interest on savings is taxable, and some loan interest may be deductible.

Common mistakes

Comparing an APR with an APY. They measure different things. Convert one to the other first.

Reading a savings APY as a loan APR. A higher number is better when you are earning, worse when you are paying.

Ignoring fees when shopping loans. The lowest stated rate is not always the cheapest loan. Compare the APR including fees.

Over-weighting compounding frequency. Daily versus monthly is a rounding error on most rates. The rate itself decides.

Assuming the rate will last. A promotional or variable rate is only a snapshot.

Frequently asked questions