Compound Growth
APY vs APR Calculator: Compounding Frequency Matters
The same nominal rate pays different interest depending on how often it compounds. At 5% compounded daily, $10,000 earns a 5.1267% APY and grows to $16,486.65 over 10 years, versus 5.0000% APY and $16,288.95 compounded annually — daily compounding is worth $197.70 more.
Currency changes the displayed symbol only — figures are not converted by an exchange rate.
Daily compoundingAnnual compounding
| Year | Daily Balance | Annual Balance |
|---|---|---|
| 0 | $10,000.00 | $10,000.00 |
| 1 | $10,512.67 | $10,500.00 |
| 2 | $11,051.63 | $11,025.00 |
| 3 | $11,618.22 | $11,576.25 |
| 4 | $12,213.86 | $12,155.06 |
| 5 | $12,840.03 | $12,762.82 |
| 6 | $13,498.31 | $13,400.96 |
| 7 | $14,190.34 | $14,071.00 |
| 8 | $14,917.84 | $14,774.55 |
| 9 | $15,682.64 | $15,513.28 |
| 10 | $16,486.65 | $16,288.95 |
A 5% rate compounded daily earns an effective 5.1267% APY, versus 5.0000% compounded annually. On $10,000 over 10 years, daily compounding is worth $197.70 more — a 0.1267-point yield gap.
Disclaimer: This calculator is provided for educational and estimation purposes only and does not constitute formal financial advice.
Two rates, one headline
APR and APY describe the same account but answer different questions. The APR is the nominal annual rate — the percentage printed on the brochure — and it ignores how often interest is credited. The APY is the effective annual yield: the rate you would need, compounding once a year, to produce the same balance the account actually produces with its real compounding schedule.
The gap between them is small enough that people routinely ignore it, which is exactly why it is worth understanding. A 5% account compounding daily does not earn 5% a year; it earns 5.1267%. That extra 0.1267 points is not interest on your money. It is interest on your interest, and it is the entire point of this page.
The formula
The effective annual yield of a nominal rate compounded n times a year is:
Where r is the nominal annual rate as a decimal and n is the number of
compounding periods per year. With n = 1 the formula returns r unchanged —
annual compounding is the baseline every other frequency is measured against.
With n = 365 it returns the daily-compounded yield loaded above.
The calculator compares those two ends of the spectrum: daily versus annual compounding. Everything between them — quarterly, monthly — falls in a narrow band that widens as the rate rises.
What the frequency actually buys you
The honest summary is that frequency is a second-order concern. On $10,000 at 5% over 10 years, daily compounding beats annual compounding by $197.70. That is real money, but it is the kind of real money that arrives $20 a year — worth having, not worth building a decision around.
The ordering flips only when the rate climbs. The same $10,000 over the same decade moves the spread as follows:
| Nominal rate | Daily-compounded APY | Dollar spread (10 yrs, $10k) |
|---|---|---|
| 1% | 1.0050% | $5.47 |
| 5% | 5.1267% | $197.70 |
| 10% | 10.5156% | $1,241.67 |
| 25% | 28.3916% | $28,588.47 |
At savings-account rates the frequency barely registers; at credit-card rates the same arithmetic works against you and becomes a meaningful part of why carrying a balance is expensive. The lesson is symmetric: compounding rewards savers and punishes borrowers, and both effects grow with the rate.
Interest in year one
To see the frequency effect in isolation, strip away the long horizon and look at a single year on a $25,000 balance at 5%:
| Compounding frequency | Periods per year | Year-one interest |
|---|---|---|
| Annual | 1 | $1,250.00 |
| Quarterly | 4 | $1,273.63 |
| Monthly | 12 | $1,279.05 |
| Daily | 365 | $1,281.69 |
Moving from annual to daily compounding adds $31.69 on a $25,000 balance over the full year. That is the entire daily-versus-annual story in one line: real, but small. The rate itself matters far more than how finely it is sliced.
Why the gap compounds
The year-one gap is tiny because it is interest on a single year’s worth of interest. The multi-year gap in the calculator is larger because every year’s frequency bonus becomes part of next year’s principal. That is the recursive definition of compounding: the balance after one period becomes the balance the next period earns on.
The calculator’s chart shows that divergence as two curves that leave the same starting point and drift apart — barely visible in the early years, then increasingly distinct. The table below the chart lists the two balances year-by-year so the spread can be read as a number rather than inferred from a slope.
How to use this comparison
Compare accounts on APY, not APR, whenever two products quote the same nominal rate but different compounding schedules. If you already have an account and want to know what more-frequent compounding is worth, keep the principal and rate fixed and extend the horizon — the dollar gap grows faster than linearly because it is compounding on itself.
Then discount the result. The spread this calculator reports is the maximum a frequency change can earn if the rate, principal, and horizon all hold exactly. Fees, a rate that changes mid-term, or an early withdrawal will each erase more than daily-versus-annual compounding ever adds. Frequency is the tiebreaker, not the decision.
The assumptions
The calculator treats the quoted rate as fixed for the whole horizon and credits interest at the stated frequency with no fees, taxes, or withdrawals. The daily path uses a 365-day year; leap years are not modeled. The annual path uses a single compounding period per year. Both paths hold the principal untouched, so the comparison isolates frequency and nothing else.
Frequently asked questions
What is the difference between APR and APY?
APR is the nominal annual rate — the simple percentage a bank quotes before compounding is applied. APY is the effective annual yield once compounding frequency is folded in. The two are equal only when interest compounds once a year; any more-frequent compounding pushes APY above APR because each interest payment begins earning its own interest sooner.
Why does daily compounding produce a higher balance than annual compounding?
Both accounts apply the same nominal rate, but daily compounding credits interest 365 times a year instead of once. Every one of those daily interest payments is added back to the balance, so each subsequent payment is calculated on a slightly larger figure. Over long horizons that small head start compounds on itself, which is exactly the dollar spread this calculator reports.
Is the APY always higher with more frequent compounding?
Yes, for any positive rate, holding everything else equal. At 0% there is no interest to compound so the frequencies tie. As the rate rises the gap widens, but the effect is modest at ordinary savings rates — the gap between daily and annual compounding at 5% is about 0.13 percentage points of yield.
Is a higher APY always the better account?
Not by itself. APY is the right figure for comparing compounding frequencies at the same quoted rate, but it says nothing about fees, liquidity, or the account actually paying the quoted rate. Chase the highest APY after matching terms you need, then check the fine print on withdrawal limits and minimum balances.
Related calculators
Compound Interest
Project monthly deposits over decades, with the formula and a year-by-year chart.
Certificate of Deposit
Maturity value, effective APY, and what an early withdrawal penalty costs.
High-Yield Savings
See in dollars what a higher APY is worth against your current rate.