APY calculator

What is an APY calculator?

An APY calculator is a free online tool that converts a nominal annual interest rate into the annual percentage yield (APY) — the real rate of return you earn in one year once the effect of compounding is included. Because interest is added to your balance several times a year and then earns interest itself, the amount you actually receive is higher than the stated nominal rate. The APY captures that difference in a single, comparable number.

Why APY matters

Banks and investment products often advertise a nominal rate, but two accounts with the same nominal rate can pay different amounts if they compound at different frequencies. APY normalises this: it tells you the effective yearly growth regardless of how often interest is credited. This makes APY the fairest way to compare savings accounts, certificates of deposit, and other interest-bearing products side by side.

How does the APY calculator work?

You provide three pieces of information:

• The nominal annual interest rate (the advertised rate).
• The compounding frequency (daily, weekly, monthly, quarterly, semiannually, or annually).
• Optionally, an account balance, so the calculator can show the interest earned in one year.

The calculator raises the per-period rate to the number of periods in a year, subtracts one, and expresses the result as a percentage. If you enter a balance, it also multiplies that balance by the APY to show the interest you would earn over a year and your balance afterwards.

Compounding frequency

The compounding frequency defines how many times per year interest is added to the principal. More frequent compounding produces a higher APY for the same nominal rate, because each new chunk of interest starts earning interest sooner. Common frequencies are:

• Daily: 365 times a year
• Weekly: 52 times a year
• Monthly: 12 times a year
• Quarterly: 4 times a year
• Semiannually: twice a year
• Annually: once a year, where APY equals the nominal rate

Formula

The annual percentage yield is calculated as:

$APY = \left(1 + \frac{r}{n}\right)^{n} - 1$

Where:

• $APY$ is the annual percentage yield (as a decimal; multiply by 100 for a percentage).
• $r$ is the nominal annual interest rate (as a decimal).
• $n$ is the number of compounding periods per year.

Examples of use

1. A savings account with a nominal rate of 5% compounded monthly:

   • Nominal rate $r$ = 0.05
   • Compounding $n$ = 12 (monthly)

   Calculation: $APY = \left(1 + \frac{0.05}{12}\right)^{12} - 1 \approx 0.051162 = 5.1162\%$

2. The same 5% nominal rate compounded daily:

   • Nominal rate $r$ = 0.05
   • Compounding $n$ = 365 (daily)

   Calculation: $APY = \left(1 + \frac{0.05}{365}\right)^{365} - 1 \approx 0.051267 = 5.1267\%$

3. With a balance of $10,000 at 5% compounded monthly (APY of 5.1162%), the interest earned in one year is about $511.62, leaving a balance of about $10,511.62.

Notes

When the compounding frequency is annual, the APY equals the nominal rate exactly, because interest is credited only once. The gap between the nominal rate and the APY widens as the rate rises and as compounding becomes more frequent. APY measures the return you earn on savings; the equivalent measure of the cost of borrowing, which also includes fees, is the annual percentage rate (APR).

Compare related tools such as the compound interest calculator and the savings plan calculator to project growth over multiple years.

FAQs

What is the difference between APY and the nominal rate?

The nominal rate is the advertised yearly rate before compounding is taken into account. The APY is the effective yearly rate after compounding, so it is always equal to or higher than the nominal rate.

Does more frequent compounding always increase the APY?

Yes. For a fixed nominal rate, increasing the compounding frequency raises the APY, although the gains shrink as you move from monthly to daily compounding and approach a limit known as continuous compounding.

How is APY different from APR?

APY describes the return earned on savings or investments and includes the effect of compounding. APR describes the cost of borrowing and typically reflects fees rather than intra-year compounding, so the two are not directly interchangeable.