Annual Percentage Rate (APR) and Annual Percentage Yield (APY) are both ways to express the annual interest rate of a financial product, such as a loan or a savings account.

APR is a measure of the annualized cost of borrowing money, including interest and fees. It is expressed as a percentage. For example, if you take out a loan with an APR of 12%, you can expect to pay 12% per year in interest on the loan.

APY is a measure of the annual return on an investment, including compound interest. It is also expressed as a percentage. For example, if you put money in a savings account with an APY of 2%, you can expect to earn 2% per year on your investment.

Here is a table to help compare the two:

APR | APY | |
---|---|---|

Definition | Annual Percentage Rate is the annual cost of borrowing money, including interest and fees. | Annual Percentage Yield is the annual return on an investment, including compound interest. |

Formula | APR = (Interest + Fees) / Principal x 100% | APY = (Ending balance – Starting balance) / Starting balance x 100% |

Example | If you take out a loan for $10,000 with an interest rate of 10% and a origination fee of $100, the APR would be: ((10,000 x 10%) + 100) / 10,000 x 100% = 11% | If you start with a balance of $10,000 in a savings account with an interest rate of 2% and you earn $200 in interest over the course of the year, the APY would be: (10,200 – 10,000) / 10,000 x 100% = 2.2% |

Here are a few more things to consider when it comes to APR and APY:

- APR is typically used to describe the interest rate on loans, such as mortgages, personal loans, and credit card loans.
- APY is typically used to describe the interest rate on financial products that earn interest, such as savings accounts, certificates of deposit (CDs), and money market accounts.
- APR is a “simple” interest rate, meaning it does not take into account the effect of compound interest. This means that if you take out a loan with an APR of 12%, you will pay 12% interest on the principal each year, regardless of how long you take to pay off the loan.
- APY takes into account the effect of compound interest, meaning that the interest you earn on your investment is reinvested and can earn additional interest. This means that if you put money in a savings account with an APY of 2%, you will earn 2% interest on the principal each year, but the total return on your investment will be higher due to the compounding effect.

For example, let’s say you take out a loan for $10,000 with an APR of 12% and a loan term of 5 years. The total cost of the loan, including interest, would be $12,000, or an additional $2,000 in interest.

#### How does compounding affect APY?

Compounding refers to the process of earning interest on an investment, and then earning interest on the interest that has been earned. This can have a significant effect on the total return of an investment over time, especially when the investment is held for a long period of time.

The frequency of compounding can affect the APY of an investment. For example, if an investment compounds interest daily, the APY will be higher than if it compounds interest annually. This is because the more frequently interest is compounded, the more opportunities there are for the investment to earn additional interest, and the higher the total return on the investment will be.

Here is an example to illustrate how compounding can affect the APY of an investment:

- Let’s say you put $1,000 in a savings account with an APY of 2% and no fees, and the interest is compounded annually. After one year, your total return would be $20, or an additional $20 in interest.
- Now, let’s say you put the same $1,000 in a savings account with an APY of 2%, and the interest is compounded daily. After one year, your total return would be $20.06, or an additional $20.06 in interest.

In this example, the difference in the APY due to the difference in compounding frequency may seem small, but it can add up over time, especially with larger investments or longer holding periods.

#### Why is compounding called 8th wonder of the world?

Compounding is often referred to as the “eighth wonder of the world” because of the powerful effect it can have on the growth of an investment over time. When an investment compounds, the interest earned on the investment is reinvested, allowing it to earn additional interest. This means that the total return on the investment can grow exponentially, rather than linearly.

For example, let’s say you put $1,000 in a savings account with an APY of 10% and no fees, and the interest is compounded annually. After one year, your total return would be $1,100, or an additional $100 in interest. If you left the investment in the account for another year, it would earn an additional $110 in interest, for a total return of $1,210. If you continued to leave the investment in the account and it continued to compound at the same rate, the total return on the investment would continue to grow exponentially over time.

The power of compounding is why it is important to start saving and investing as early as possible. The longer an investment has to compound, the more time it has to grow, and the larger the total return on the investment can be.

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