APY Calculator

What APY actually measures

APY answers one question: if you put money in and leave it for exactly one year, what percentage will you have gained, counting every compound of interest along the way? A bank advertising 5% APY promises $500 per year per $10,000. A bank advertising a 5% rate without saying APY is quoting the nominal rate, and the true yield depends on how often that rate compounds.

The distinction matters most when compounding is frequent. At annual compounding, nominal and APY are identical. At monthly they diverge slightly; at daily, slightly more. The APY number is the honest one, which is why United States depository institutions are required by the Truth in Savings Act to disclose it.

How compounding frequency changes the yield

Each time interest compounds, it starts earning its own interest. Compounding annually gives interest one chance per year. Monthly gives twelve, daily gives three hundred sixty-five. Each increase in frequency adds a little yield, but the increments shrink fast: 5% nominal is 5.00% APY annually, about 5.12% monthly, about 5.13% daily.

This is why the difference between daily and continuous compounding is worth pennies on a $10,000 balance, while the difference between a 4.50% and a 5.00% APY is worth $50. Frequency is a rounding error next to the rate itself. Shop by APY first, frequency second.

APY versus APR

APY and APR are both annualized rates, but they run in opposite directions. APY is what you earn; it accounts for compounding in your favor. APR is what you pay on a loan; it accounts for fees and compounding in the lender's favor. Savings ads quote APY, loan ads quote APR, and both are quoted in the form that flatters the advertiser.

When comparing deposit accounts, convert everything to APY. When comparing loans, compare APR, and read the fee schedule: two loans with the same APR can differ in total cost if one front-loads fees.

The effect of monthly contributions

Contributions change the math more than most people expect, because each deposit starts compounding on the day it lands. Adding $200 a month at a 5% nominal rate compounded monthly yields a 5.1162% APY and ends year one at $2,466.00, of which $66.00 is interest on money that was only in the account for part of the year.

Over long horizons the contribution stream dominates the principal. Twenty years of $200 monthly deposits is $48,000 contributed; at the same monthly-compounded 5% rate it grows to $82,549.26, of which $34,549.26 is interest. The earlier each deposit lands, the more years it compounds, which is the entire argument for automating savings on payday rather than in a year-end lump.

Worked scenarios: $10,000, $25,000, and $200 per month

The tables below are scenario paths the calculator reproduces directly from its formula at a 5.00% nominal rate. They show how the same compounding mechanics scale with balance size and with time more than with frequency: moving from annual to daily compounding adds $11.67 on a $10,000 balance in one year, while moving from one year to ten years adds about ten times the whole balance in interest.

The growth table holds the deposit steady and varies the term. Because each year's interest joins the following year's base, the yearly gain accelerates: $10,000 at the 5.1162% monthly APY gains $511.62 in year 1, $1,641.63 in year 10, and $3,460.49 between years 29 and 30. Every figure in both tables is computable from APY = (1 + r/n)^n - 1 compounded forward; none is a quoted bank offer.

Growth of $10,000 at the 5.1162% monthly APY

This table holds the frequency fixed (monthly) and scales the term, so it answers the question the frequency table cannot: how long does compounding need before the interest column overtakes the principal? The gain crosses $10,000, equal to the original deposit, between years 14 and 15 under these scenario assumptions.

$200 a month of new deposits compounds faster than either table shows, because each deposit carries its own compounding clock. Twenty years of $200 monthly deposits at this APY reaches $82,549.26 on $48,000 contributed, and thirty years reaches $177,145.28 on $72,000: the interest portion outgrows the deposits in the final decade.

Using the calculator well

Enter the APY, not the nominal rate, when the bank shows both. Set compounding frequency to match the account: savings accounts typically compound daily and pay monthly, CDs compound and pay on their stated schedule. Check that deposit and contribution fields match how you actually save.

The projection assumes the rate holds for the whole term. Variable-rate savings accounts reprice when the Federal Reserve moves, so treat long projections at today's APY as a scenario, not a forecast. For rate-risk planning, run the projection at a rate one point lower and see whether the plan still works.

Assumptions and limits

Results assume interest compounds at the entered frequency with no missed payments, no withdrawal penalties, and no taxes on interest. Interest earnings are taxable as ordinary income in most cases, which lowers the effective after-tax yield. The tool is an educational calculator, not tax or investment advice.