APY (Annual Percentage Yield) is a compound interest rate owned on a deposit over one year. It accounts the interest earned on principal as well as interest earned on other earnings and is referenced as the effective annual rate in finance.

Annual Percentage Yield assumes that all the funds will remain in the investment and investor would not add or withdraw any funds during this year. It is an instrument which gives you an idea of how much interest your money will earn. By knowing APY you can decide which bank has the best offer.

The advantage of the Annual Percentage Yield is the fact, that it takes into account compounding, which is interest on interest. In other words, it’s the amount of interest earned on the investment where the amount earned is reinvested rather than being paid out. By using compound interest, you get a faster increase in the value of capital than by using simple interest.

Annual Percentage Yield (APY) shows such an annual interest rate as if the annual compound interest was compounded once a year and would give the same increased value (future value) as while calculating the annual compound interest that is compounded several times per year.

If you’re the one who earns interest (i.e. savings account), higher APY is more preferable to you. Consequently, if you pay the interest (i.e. loan), a lower Annual Percentage Yield is better for you.

### How to Calculate Annual Percentage Yield?

Annual Percentage Yield is calculated as:

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

Where r = annual interest rate and n = number of compounding periods per year (i.e. monthly compounding – 12, quarterly – 4, semi-annually – 2, annually – 1) .

As it results from the formula, the effective annual interest rate depends primarily on:

• The nominal annual interest rate
• The number of compounding periods per year – occurring both in the exponent and in the denominator of the fraction

Note that the amount of payment has no impact on Annual Percentage Yield, so it’s not used in this formula.

This formula is the same as Effective Annual Interest Rate which has the same purpose – to determine actual earnings or payments on financial products such as loans, mortgages, savings accounts, deposit certificates, and others.

### Conclusions Resulting from the Analysis of the Formula

• Annual Percentage Yield is equal to the Nominal Rate only if compounding happens once a year
• Annual Percentage Yield is higher than the Nominal Rate if the compounding period is shorter than one year
• APY is the higher the more times the rate compounds over a year
• APY is the highest in case of continuous compounding which is an extreme case of compounding, when the time gap between the compounding periods drops to zero

#### Example of Annual Percentage Yield Calculation

Let’s assume your bank proposes you two investments.

• Investment A offers you the nominal rate of 3%, annually compounded monthly.
• Investment B offers you the nominal rate of 3.2% annually, compounded quarterly.

Annual Percentage Yield is the instrument which allows to compare these investments.

$APY_{A} = \left(1 + \frac{3\%}{12}\right)^{12} - 1 = 3.04\%$$APY_{B} = \left(1 + \frac{3.2\%}{4}\right)^{4} - 1 = 3.02\%$

Despite the fact, that a nominal interest rate offered by Investment B was higher than offered by Investment A, your capital will actually grow by 3.04% if you Invest in A, and only by 3.02% if you invest in B because the rate compounds fewer times over the year. The difference may seem insignificant, but over many years or/and with big investments, the difference becomes more substantial.

### Other Methods of Interest Rates Comparison

Annual Percentage Rate is another popular method of financial instruments comparison. In some situations, APR is more accurate, because it calculates a rate which includes fees and charges. It can be used to calculate the actual cost of a loan. However, it doesn’t take compounding into account, so you may want to calculate both APR and APY to understand the actual price of the loan.

APR is calculated as:

$APR = \frac{ \frac{P \times r \times n } {100} + c }{ (P \times n) } \times 100$

Where P = the principal loan amount, r = the interest rate per period, n is the number of periods and c = any finance charges/fees.