APR is the annualized cost or rate of borrowing, stated without compounding; APY is the effective yearly return on a deposit after compounding. In plain English, APR shows the rate before interest-on-interest is included, while APY shows what one year of compounding can produce. The difference matters because more frequent compounding usually creates a higher effective return.
How it works
Both terms put a rate on a one-year basis, but they treat compounding differently. A nominal annual rate is stated before interest-on-interest. If it is 12%, 12% is the starting point; any return from compounding must be added separately.
- Take the stated annual rate and divide it by the number of compounding periods.
- Add that period rate to 1, then multiply the result by the balance.
- Repeat the calculation for every compounding period in the year.
- Compare the ending balance with the starting balance to find the effective annual return.
Mathematically, if r is the nominal annual rate and n is the number of compounding periods, APY equals (1 + r ÷ n) raised to the power n, minus 1.
Think of a 12% rate with monthly compounding as 1% each month. Without monthly crediting, simple annual interest would be $120 on $1,000. With monthly crediting, however, the second month’s interest applies to a slightly larger balance. APY combines all those monthly effects into one annual percentage.
What “APR” means. APR is generally a non-compounded annualized measure. For revolving credit, it shows the annual cost of carrying a balance rather than a compounded investment return. For an instalment loan, the disclosed APR often includes interest plus certain upfront or ongoing charges. That is why “simple annual rate” is a useful shorthand, but not a complete description of every loan APR. Not all charges are included, and treatment can vary by jurisdiction and disclosure.
An advertised APY usually assumes that the money stays invested for a full year, compounding continues, and the rate does not change. Withdrawals, fees, taxes, or a changing rate can make the actual result lower than the advertised APY.
A worked example of compounding
Assume a $1,000 deposit earns a 12% nominal annual rate for one full year, with no fees or withdrawals. The compounding frequency changes, but the nominal rate does not.
- Annual compounding: The entire 12% is credited once. The balance becomes $1,000 × 1.12, or $1,120. The $120 gain equals 12% of the original deposit, so the APY is 12.00%.
- Quarterly compounding: Each quarter adds 3%. Four periods give $1,000 × 1.03 × 1.03 × 1.03 × 1.03, or $1,125.51. The effective return is $125.51 on $1,000, producing an APY of 12.55%.
- Monthly compounding: Each month adds 1%. Repeating that calculation for 12 months gives $1,126.83. The effective return is $126.83 on $1,000, producing an APY of 12.68%.
The order is annual, then quarterly, then monthly: at the same nominal rate, more frequent compounding produces a higher APY. Monthly compounding adds $6.83 compared with annual compounding over this year. That extra amount comes from earning interest on interest, not from a higher stated rate.
APY is derived from the actual crediting pattern; it is not simply a number placed beside the nominal rate. If interest is credited once a year at 12%, the APY remains 12%. If it is credited monthly, the effective annual return becomes 12.68% under these assumptions.
Where each rate appears, and why
The labels are usually chosen to match the transaction being described.
- Loans and credit cards: Loan and credit-card disclosures commonly use APR. A credit-card APR is the annualized interest rate charged on a balance. A mortgage, auto loan, or personal loan may show both an interest rate and an APR that incorporates certain fees. Comparing the interest rate alone can therefore miss part of the borrowing cost.
- Savings and deposits: Savings accounts, certificates of deposit, and money market accounts generally highlight APY because it includes the effect of compounding. A certificate of deposit may also carry an early-withdrawal penalty, while a promotional account may require certain balances or deposits. Those terms do not disappear because the APY looks attractive.
APR gives borrowers a common annual measure of credit cost. APY gives savers a common annual measure of return, including compounding. That is also why lenders and banks often present the underlying rate and the broader annual measure together. The wording is not evidence that one institution is being more generous; the metrics answer different questions.
How to compare offers fairly
A fair comparison starts with matching the metric to the decision and checking the assumptions behind it.
- Compare savings with savings and loans with loans. Use APY to compare deposit returns and APR to compare borrowing costs. Do not treat a savings APY as directly comparable with a loan APR.
- Check the conditions. Determine whether compounding is daily, monthly, quarterly, or annual. Also check for a bonus rate, minimum-balance requirement, automatic-renewal condition, or direct-deposit requirement.
- Include borrowing fees and term. For loans, consider mandatory origination, application, and other disclosed charges alongside the APR. A lower APR can still cost more if fees are higher or the repayment period is longer.
- Account for deposit restrictions. Review withdrawal penalties, interest-crediting frequency, compounding frequency, and fees that reduce the balance. An APY generally describes the return before taxes, so the after-tax result may be lower.
- Distinguish fixed, variable, and promotional rates. A headline APY may apply only temporarily, while a credit-card APR may change. Confirm what rate applies after an introductory period and how often it can be adjusted.
No single headline number captures the whole deal. APR can conceal fees; APY can conceal conditions, penalties, taxes, or the possibility that a variable rate will fall. Inflation also matters: a positive APY means the nominal balance grows, but it does not guarantee an increase in purchasing power. The fairest comparison uses consistent assumptions and focuses on the dollars you will earn or repay, not just the largest percentage.
This is general information, not financial advice. Rates, fees, taxes, penalties, and product terms vary, so review the current disclosure for any offer being considered.
Key takeaways
- APR is primarily a borrowing measure; APY is primarily an earning measure.
- At the same nominal rate, more frequent compounding generally produces a higher APY.
- APR does not show compounding in the same way APY does, and a loan APR may include certain fees.
- Compare like with like and account for fees, taxes, penalties, rate changes, and timing.
- The highest advertised percentage is not necessarily the best deal once all conditions are considered.
Frequently asked questions
Are APR and APY directly comparable?
No. They measure different transactions and use different calculations. Use APY to compare the effective return on savings accounts and APR to compare the annualized cost of credit. A lower borrowing cost is desirable, while a higher deposit return is desirable, but only after fees, access, penalties, and other terms are considered.
Why is APY higher than the nominal rate?
Positive compounding means interest is added to the balance and then earns additional interest. With a 12% nominal rate, quarterly compounding produces a 12.55% APY, while monthly compounding produces 12.68%. The underlying nominal rate is still 12%; APY shows its effective annual result under the stated compounding assumptions.
Does APR include fees or compounding?
A loan’s APR may include certain fees, depending on applicable rules and disclosure, but it generally does not show the growth generated by compounding. This is why APR is used for annualized borrowing comparisons, while APY is used to describe the effective return on a deposit.
Is the highest APY always the best savings choice?
No. The APY may depend on a minimum balance, promotional setup, variable rate, or other conditions. Early-withdrawal penalties, fees, taxes, and how quickly you can access the money also matter. Read the current disclosure and compare offers over a holding period that matches your realistic plans.
