APY Calculator

To calculate your APY and project savings growth, follow these steps:

1. Enter Principal Amount: This is your starting balance or initial lump sum deposit. It could be an existing savings account balance, a CD deposit, or any amount you plan to start with. Even a modest starting amount benefits from compounding over time.
2. Enter Annual Interest Rate (APR): This is the stated annual percentage rate offered by your bank or financial institution. You can find this on the account details page of your bank's website or in your account agreement. Do not enter the APY here, as this calculator computes the APY for you from the APR.
3. Select Compounding Frequency: Choose how often your account compounds interest. Most high-yield savings accounts use daily compounding. CDs may compound daily or monthly. Check your account terms if you are unsure. Selecting different frequencies lets you compare how compounding impacts your returns.
4. Enter Monthly Deposit Amount (Optional): If you plan to make regular monthly contributions to your savings, enter that amount here. Consistent monthly deposits are one of the most effective ways to accelerate savings growth and take full advantage of compounding.
5. Enter Time Period: Specify how many years you plan to keep the money in the account. Longer time periods demonstrate the exponential nature of compound growth, with interest earnings accelerating dramatically in later years.

After entering your details, review the calculated APY, final balance, total deposits made, and total interest earned. Use the growth chart to visualize how your savings build over time. To compare bank offers, run the calculator with different APR values and compounding frequencies to see which option produces the highest final balance.

Annual Percentage Yield (APY) is the real rate of return you earn on a savings account, certificate of deposit, or other interest-bearing account over one year, taking into account the powerful effect of compound interest. APY is the number that truly matters when evaluating where to park your money, because it reflects not just the base interest rate but how often that interest compounds, which directly impacts how much you actually earn.

The critical distinction every saver should understand is the difference between APY and APR (Annual Percentage Rate). APR is the simple, stated interest rate without any compounding factored in. APY, on the other hand, includes the effect of compounding, meaning interest earned on previously earned interest. For example, a savings account advertising a 5.00% APR with daily compounding actually delivers an APY of approximately 5.13%. That 0.13% difference may seem small, but on a $50,000 balance it translates to an extra $65 per year in earnings with no additional effort. The more frequently interest compounds, the wider the gap between APR and APY becomes.

Compounding frequency is the key factor that determines how much APY exceeds APR. With daily compounding (365 times per year), interest is calculated and added to your balance every single day, meaning each subsequent day's interest calculation includes the previous day's earned interest. Monthly compounding (12 times per year) adds interest once per month, quarterly compounding (4 times per year) every three months, and annual compounding (once per year) provides the least benefit since interest is only calculated once. The practical differences between daily and monthly compounding are modest, but both significantly outperform annual compounding over long time periods.

For savings accounts and CDs, APY is especially important because it allows you to make apples-to-apples comparisons between financial institutions. High-yield savings accounts at online banks currently offer APYs in the 4-5% range, dramatically outperforming traditional brick-and-mortar banks that may offer just 0.01% to 0.10% APY. CDs often offer slightly higher APYs in exchange for locking your money up for a fixed term. Understanding APY empowers you to ensure your savings are working as hard as possible and not losing purchasing power to inflation.

The core formula for calculating Annual Percentage Yield is:

APY = (1 + r/n)n − 1

Compound Balance (no deposits):

Balance = Principal × (1 + r/n)n × t

Future Value of Regular Deposits:

FV = PMT × [((1 + r/n)n × t − 1) / (r/n)]

Where PMT is adjusted to the deposit per compounding period (monthly deposit × 12 / n).

Total Interest Earned:

Interest = Final Balance − Total Deposits

The APY formula reveals why compounding frequency matters: as n increases, (1 + r/n)ⁿ approaches the mathematical constant e^r, which represents continuous compounding. For a 5% APR: annual compounding yields 5.00% APY, quarterly yields 5.09%, monthly yields 5.12%, and daily yields 5.13%. The jump from annual to quarterly is the largest marginal gain, with diminishing returns beyond monthly compounding.

Example 1 - Daily vs Annual Compounding: You deposit $10,000 into a savings account with a 5.00% APR for 10 years with no additional deposits. With daily compounding: APY = 5.13%, and your balance grows to $16,487, earning $6,487 in interest. With annual compounding: APY = 5.00%, and your balance grows to $16,289, earning $6,289 in interest. The daily compounding advantage is $198 over 10 years on this deposit. While modest for a single deposit, the difference compounds further with larger balances and longer time periods.

Example 2 - Monthly Deposits with Daily Compounding: You start with $5,000 and add $300 per month to a high-yield savings account offering 4.75% APR with daily compounding. APY = 4.87%. After 5 years: total deposits = $5,000 + ($300 × 60) = $23,000. Final balance = $26,218. Total interest earned = $3,218. After 10 years: total deposits = $41,000. Final balance = $50,328. Total interest earned = $9,328. Notice how interest earnings accelerate in the second five years ($6,110) compared to the first five years ($3,218), demonstrating the exponential nature of compounding.

Example 3 - Comparing Bank Offers: You have $25,000 to deposit and want to compare three options over 3 years. Bank A: 4.50% APR, daily compounding. APY = 4.60%. Final balance = $28,631. Interest earned = $3,631. Bank B: 4.60% APR, monthly compounding. APY = 4.70%. Final balance = $28,732. Interest earned = $3,732. Bank C: 4.75% APR, quarterly compounding. APY = 4.84%. Final balance = $28,857. Interest earned = $3,857. Bank C offers the best return despite quarterly compounding because its base APR is the highest. This demonstrates that while compounding frequency matters, the base APR rate is usually the more important factor when comparing accounts. Always compare the advertised APY, not just the APR, to make the most informed decision.