APY Calculator – Loan calculator

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Reviewed by: Anya Sharma, MBA, Certified Financial Planner (CFP)
Anya Sharma is a CFP and financial strategist ensuring the accuracy of effective rate conversions for consumer finance.

Use the authoritative **APY Calculator** to convert a bank’s stated nominal interest rate and compounding frequency into the true rate of return, the Annual Percentage Yield (APY). Simply enter any three variables—APY, Nominal Rate, or Compounding Frequency—to solve for the remaining unknown value.

Annual Percentage Yield (APY) Calculator

F: Annual Percentage Yield ($\mathbf{APY}$, %)

P: Annual Interest Rate ($\mathbf{r}$, Nominal, %)

V: Compounding Frequency ($\mathbf{n}$, Times per Year)

APY Formula

Core APY Relationship:

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

The solution formulas:

APY (F) $= \left[\left(1 + \frac{r}{n}\right)^n – 1\right] \times 100$

r (Nominal Rate, P) $= \left[n \times \left((1 + APY)^{1/n} – 1\right)\right] \times 100$

n (Frequency, V) is solved iteratively from the APY formula.

Formula Source: Investopedia

Formula Variables

F ($\mathbf{APY}$): Annual Percentage Yield. The true rate of return earned in one year, including compounding.
P ($\mathbf{r}$ – Nominal Rate): The stated annual interest rate (before compounding effect).
V ($\mathbf{n}$ – Frequency): The number of times interest is compounded per year (e.g., Monthly = 12).
Q (Principal – Hidden): A fixed placeholder value of $1 used to derive the rate based on a single year.

Related Calculators

What is APY?

Annual Percentage Yield (APY) is the standardized metric used in finance to represent the real rate of return on an investment or savings account. Unlike the Nominal Rate, which is simply the stated rate, APY includes the effect of **compounding**, meaning interest earned on interest. This makes APY the definitive way to compare different financial products, regardless of their compounding frequency.

The difference between the Nominal Rate and the APY increases as the compounding frequency ($n$) increases. For example, a 5% rate compounded annually is exactly 5% APY, but the same 5% rate compounded monthly yields an APY slightly higher than 5%. Financial institutions are required by law (in many jurisdictions) to disclose the APY so consumers can make apples-to-apples comparisons.

How to Calculate Required Nominal Rate (Example)

Let’s find the Nominal Rate (P) required to achieve an APY (F) of $6.0\%$ when compounding occurs Monthly (V=12).

Step 1: Determine Variables
$APY = 0.06$. $n = 12$ (Monthly compounding).
Step 2: Apply the Nominal Rate Formula
The formula for $r$ (decimal) is $r = n \times [(1 + APY)^{1/n} – 1]$.
Step 3: Calculate the Growth Factor
Growth Factor: $(1 + 0.06)^{1/12} \approx 1.00486755$
Step 4: Determine the Nominal Rate
$r = 12 \times (1.00486755 – 1) \approx 0.05841$. The Nominal Rate (P) required is **5.84\%**.

Frequently Asked Questions (FAQ)

What is the difference between APY and APR?

APY (Annual Percentage Yield) is the effective rate that includes compounding, typically used for savings accounts and investments. APR (Annual Percentage Rate) is the simple, nominal rate, typically used for loans and mortgages (though loans also often compound, APR does not include that effect in its stated rate).

Does continuous compounding exist?

Mathematically, yes. Continuous compounding is the theoretical limit as the compounding frequency ($n$) approaches infinity. The formula uses Euler’s number ($e$) and is $APY = e^r – 1$. This calculator includes a continuous compounding option.

Why is the calculated APY always higher than the Nominal Rate (r)?

When interest compounds more than once a year ($n > 1$), the interest earned in early periods begins earning interest itself in later periods. This compounding effect causes the effective rate (APY) to be higher than the stated nominal rate ($r$).

Is APY used for loans?

For loans, the equivalent effective rate is the Effective Annual Rate (EAR), which is mathematically the same as APY, but is rarely disclosed to consumers in the same clear way APY is for savings.

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