APY Calculator

How does this APY calculator work?

The financial tool estimates the APY for your deposit by taking account of the variables that should be provided:

• Stated Annual Interest Rate (r) which is the nominal rate of return the bank offers.
• Term / number of periods (t) you deposit your cash. It can be either as a number of months or years.
• Compounding frequency (n) is the rule that shows how often the interest gets capitalized and can be Daily (365 times/year), Monthly (12 times per year), Quarterly (4 times/year), Semi-annually (two times per year) or Annually (once every year).
• Deposit / Principal amount (P) is an optional info where you can input your savings.

The algorithm behind this APY calculator uses the formulas explained below:

1)   APY formula calculation:

- IF (t) is specified as a no. of years THEN APY = [((1 + ((r * 0.01) / (n * t))) ^ (n * t)) – 1] * 100

- IF (t) is expressed in months THEN APY = [((1 + ((r * 0.01) / (n * t / 12))) ^ (n * t / 12)) – 1] * 100

2) Ending balance equation = P * (1 + APY%)^(t in years)

3) Total interest earned = Ending Balance – P

What is APY?

In finance APY is the acronym for Annual Percentage Yield and represents the normalized interest rate by its compounding frequency within one year. In other words APY is the right figure to look at when comparing multiple bank offers that have different compounding interest rules.  Please note that this indicator does not take account of the fees and charges the financial institution may apply, thus in order to have an even better image of the net gain of a depositor you should consider them as well.

Please remember that the APR (annual percentage rate) differ from the APY, as the first one is the effective interest rate paid by borrowers to financial institutions, while APY is the effective rate of return paid by the financial institution to the depositor.

Example of a calculation

Scenario 1: Assuming a bank offers a nominal interest rate of 2.5% compounded daily how much will someone end up with in account for a deposit of $10,000 over 2 years?

■ Annual Percentage Yield (APY) = 2.5315%

■ Ending Balance = $10,512.70

■ Total Interest Earned = $512.70

Scenario 2: What is a better offer for depositing $1,000 for a year: 3.4% interest rate compounded monthly or 3.39% compounded daily?

- 1st offer results

■ Annual Percentage Yield (APY) = 3.4535%

■ Ending Balance = $1,034.53

■ Total Interest Earned = $34.53

- 2nd offer results

■ Annual Percentage Yield (APY) = 3.4480%

■ Ending Balance = $1,034.48

■ Total Interest Earned = $34.48