Annual Percentage Yield

Annual percentage yield (APY) can be defined as the actual rate of return on investment by considering the compounding effect. Under an APY, the calculation is done periodically, and the interest is added back to the balance, making further interest payments greater than previous ones.

Compounding can be done daily, weekly, quarterly, half-yearly, or annually. However, the higher the number of times compounding is done, the higher the APY, meaning higher returns to investors. Calculating APY facilitates easier comparison of multiple investments with different return rates, compounding frequency, etc.

• Annual percentage yield can be referred to as the real rate of return on deposits, investments, and savings accounts computed by considering the time, interest rate, and, most importantly, the compounding effect.
• APY can often be confused with the annual percentage rate (APR), but the latter is calculated on loans while the former is on investments.
• Due to the complexity of calculations, annual percentage yield calculators are available online that are helpful to a great degree.
• APY is a significant concept that is often overlooked in decision-making.

Annual percentage yield is an important parameter in finance and banking. Mostly, investors and depositors look at the interest rate, the investment period, etc., but they fail to consider the compounding effect. APY can give a holistic and comprehensive view of the actual returns one can expect from an investment.

APY is similar to the normal interest rate calculation. But it is not the same. Let’s see how. Assume that a person has a savings account. They get 10% interest on the deposit, and the compounding is done yearly. So, if initially ‘P’ amount was deposited, the interest will be 0.1 P. The account balance now would be 1.1 P. Assuming no withdrawals were made, the amount remains as such until compounded the next time, when it becomes 1.21 P (this is because the interest is calculated on the initial investment plus the last term’s interest). After that, this amount becomes 1.331 P and later 1.4641 P, and so on.

If the account were subject to simple interest calculation, P would become 1.1 P, then 1.2 P, 1.3 P, 1.4 P, etc. Thus, as can be seen, the compounding effect cannot be ignored, especially in the long run. However, this often happens when people calculate the future value of their investments. As a result, they overlook the compounding effect. This can be extremely disadvantageous in decision-making.

The APY depends on the interest rate and compounding frequency of the institution. In the United States, the Federal Deposit Insurance Corporation (FDIC) estimates the average annual percentage yield on savings accounts as 0.24%. Salem Five Direct offers the highest APY at 4.10%. Online banks generally pay more than traditional national banks. For example, Bank of America pays somewhere between 0.01% and 0.04%.

APY And APR

It is important to note that APY is different from APR – annual percentage rate. The logic underlying both concepts is the same. However, APR calculates the effective amount a borrower will pay over the course of the loan. Another important point is the annual percentage yield on crypto. Cryptocurrencies can yield as high as 10% and around 6% on average. 

The formula for APY is as follows:

Annual percentage yield = ny – 1

Here, r is the rate of return or interest.

n is the number of times compounding is done per year.

y is the number of years.

Next, how to determine the final amount?

A = I ny

A is the final amount.

I is the initial investment.

This is the general formula for finding the interest when compounding is done n times a year.

Let’s understand APY with a few examples.

Example #1

Alex deposits $500 for ten years at 10% interest, compounding done annually. How much would he receive at the end of his investment period?

First, let’s begin by calculating the APY. 

r = 10% = 0.1

n = 1

APY = 10 – 1

= 1.1046 – 1 

= 0.1046

A = (500 x 0.1046) + 500

= $552.3

Alternatively, the final amount formula can be directly used.

A = 500 10

= $552.3

Example #2

Let’s prove that the greater the compounding, the higher the returns.

Cara wants to invest $1000 in a savings account that pays 5% interest for five years. Calculate the final amount if compounding is done - every moment, every day, every month, quarterly, half-yearly, and annually.

(i) Every moment

A = Ieyr

Here, e is the Euler’s number, which equals 2.71828…..

A = 1000 (2.71828)0.25

= $1284.025

(ii) Every day

A = I 365y

= 1000 1825

= $1284.0034

(iii) Every month

A = I 12y

A = 1000 60

= $1283.35

(iv) Quarterly

A = I 4y

= 1000 20

= $1282.037

(v) Half-yearly

A = I 2y

= 1000 10

= $1280.084

(vi) Annually

A = I y

= 1000 5

= $1276.28

From this, it can be seen that the higher the compounding frequency, the higher the returns.

Considering the complexity of this calculation, annual percentage yield calculators are available online that enable users to enter the input and give them the result.

This has been a guide to Annual Percentage Yield and its meaning. Here, we explain the topic in detail, including its calculation, formula, and examples. You can learn more about accounting from the following articles –

• High-Yield Savings Account
• Nominal Yield
• Annualize