APY Calculator: APR to APY Conversion
Enter your nominal annual rate, compounding frequency, deposit amount, and time horizon. The calculator converts APR to APY using the standard (1 + r/n)^n formula, shows your final balance and interest earned, and breaks down how different frequencies compare side by side.
APY by frequency at 4.5% nominal
APY (effective annual yield)
4.594%
vs 4.5% nominal — compounded monthly
Final balance
$12,517.96
Interest earned
$2,517.96
Balance trajectory
Year-by-year breakdown
| Year | Balance | Interest |
|---|---|---|
| 1 | $10,459.40 | $459.40 |
| 2 | $10,939.90 | $939.90 |
| 3 | $11,442.48 | $1,442.48 |
| 4 | $11,968.14 | $1,968.14 |
| 5 | $12,517.96 | $2,517.96 |
How it works
APR (Annual Percentage Rate) is the stated nominal rate — the number banks quote on savings accounts and loans before compounding is taken into account. APY (Annual Percentage Yield) is the effective rate after compounding is applied. Banks are not neutral in which figure they promote: on loans they tend to quote APR because it sounds lower, while on savings products they advertise APY because it sounds higher. Neither number is dishonest on its own, but comparing a loan APR to a savings APY is an apples-to-oranges mistake that can make a product look more or less attractive than it really is.
The APY formula is APY = (1 + r/n)^n − 1, where r is the nominal rate as a decimal and n is the number of compounding periods per year (365 for daily, 12 for monthly, 4 for quarterly, 1 for annually). At each period your balance grows by a factor of (1 + r/n), and after n periods that factor has been multiplied by itself n times — which is why the exponent equals n. The final balance after t years is simply deposit × (1 + r/n)^(n × t), the same base expression raised to n × t instead of just n.
Increasing compounding frequency does raise APY, but with steeply diminishing returns. Going from annual to monthly compounding on a 5 % nominal rate lifts APY from 5.000 % to 5.116 % — a gain of 0.116 percentage points. Switching further from monthly to daily adds only another 0.011 percentage points (5.116 % to 5.127 %). The mathematical ceiling for infinite compounding (continuous compounding) is e^r − 1, which for 5 % is 5.127 %. In practice, the difference between daily and continuous compounding is so small it is unmeasurable in your actual balance, so chasing higher compounding frequency is far less important than securing a higher nominal rate.
Frequently asked questions
Why does my bank quote both APR and APY?+
Regulations in many countries — including the US Truth in Savings Act — require savings accounts to disclose APY so consumers can make apples-to-apples comparisons. But lenders often lead with APR on loan products because the number is smaller. When you see both figures on a savings account, APR is the raw input rate and APY is what you actually earn after compounding. The gap between them is a reliable indicator of how aggressively the account compounds: a 5.00 % APR with 5.13 % APY means daily compounding; the same APR with 5.12 % APY indicates monthly. Always compare accounts using APY, not APR, to get a fair comparison of yield.
Is daily compounding much better than monthly?+
Honestly, no — the difference is marginal. At 5 % nominal, daily compounding yields 5.127 % APY versus 5.116 % for monthly: a gap of just 0.011 percentage points. On a $10,000 deposit over one year that is roughly $1.10 in extra interest. Over 10 years the difference compounds to about $13 on a starting balance of $10,000. The real lever that moves your balance is the nominal rate, not the compounding frequency. A savings account offering 4.50 % compounded daily yields less than one offering 4.60 % compounded monthly. Focus on the rate; treat compounding frequency as a tie-breaker at best.
Do savings account rates change after I open the account?+
For most high-yield savings accounts and money market accounts: yes. These are variable-rate products, meaning the bank can lower (or raise) the rate at any time, often in response to central bank policy changes. Only fixed-term products like certificates of deposit (CDs) lock in the rate for the full term. This calculator uses whatever nominal rate you enter and holds it constant across all years — a simplification that works well for short planning horizons and fixed-rate products, but that will overstate returns on a variable-rate account if rates fall. For long-term projections under variable rates, consider running the calculator with a conservative (lower) rate scenario alongside your best estimate.