In the realm of personal finance, phrases such as annual percentage rate, also known as APR, and annual percentage yield, also known as APY, are often encountered. The annual percentage rate (APR) is often used to measure the expenses of loans, while the annual percentage yield (APY) is typically used to measure the return on investments. In this post, we will go over the properties of each, as well as how they are utilized and how the calculations are done for each.
Annual Percentage Rate (APR)
The annual percentage rate, or APR, is the rate that a borrower will pay each year on their debt. The APR is distinguished by the following two qualities:
- APR includes fees and other loan-related costs on top of the interest that was accrued throughout the course of the loan. This is significant because it provides customers with a more accurate representation of the overall cost of the loan they are considering.
- APR uses simple interest, not compound interest, in its calculation. The term “compound interest” refers to interest that is gained on interest already earned. Because certain loans accumulate the interest that is due, the effective rate that a customer pays on their loan could be greater than the annual percentage rate (APR) that is quoted for the loan.
Where APR is Used
When a customer is shopping around for and comparing various kinds of consumer loans, such as a vehicle loan, a home loan, or a loan on major household expenditures like appliances, the annual percentage rate (APR) is the one that is most likely to be mentioned. Consumers have the ability to compare the APRs of various kinds of loans. When comparing two different auto loans, one may utilize the annual percentage rate (APR) to determine which of the loans will result in a cheaper overall cost.
It is essential to have a clear understanding that the annual percentage rate, or APR, is distinct from, and often greater than, the basic interest rate that may be offered for a loan.
How an Annual Percentage Rate Works
The APR relies on two primary inputs:
- The charges and fees that are linked with taking out the loan.
- The interest fees associated with the loan.
After these two factors have been determined, it will be possible to compute the APR.
APR Formula & Calculation
APR = [(((Loan Fees + Loan Interest) / P) / N) * 365] * 100
- Loan Fees = The total amount of all loan fees
- Loan Interest = The entire amount of interest that is due throughout the course of the loan’s duration.
- P = The Loan Principal, often known as the total amount borrowed
- N =the entire amount of time that the loan will be in effect, measured in days
Let’s imagine a customer wants to buy a new refrigerator, so they take out a loan for $1,000 to pay for it. The following are some of the qualities of the loan:
- The main amount of the loan is $1,000.
- The loan has an interest rate of 7% per year.
- The interest on the loan comes to $70 ($1,000 multiplied by 7%).
- The overall costs linked with the borrowing come to a total of $20.
- The duration of the loan is one year.
The annual percentage rate (APR) of the customer is computed as follows:
APR = [(((20 + 70) / 1000) / 365) * 365] * 100 = 9%
Therefore, even though the interest rate on the loan was just 7%, the customer would end up paying 9% since there were other expenses involved with the transaction.
Key Takeaway: The annual percentage rate (APR) is a more precise measurement of the cost of a loan to a borrower.
Annual Percentage Yield (APY)
The annual percentage yield (APY) of an investment product is a measure that is often used for financial instruments such as savings accounts, money market accounts, and certificates of deposit (CDs). It is important to keep in mind that, in contrast to APR, APY does take compound interest into consideration.
Where is APY Used
When researching and analyzing the yields offered by a variety of savings accounts and certificates of deposit (CDs), investors will most likely come across the annual percentage yield (APY).
How an Annual Percentage Yield Works
The annual percentage yield is calculated using two factors:
- the interest rate on the investment.
- The number of times that compounding occurs.
The annual percentage yield (APY) will be higher if compounding occurs more often.
APY Formula and Calculation
APY = [(1 + (i/N)) ^ N] – 1
- i = the yearly percentage rate of return that is advertised for the investment product.
- N = the total number of times a year that compounding occurs.
Let’s imagine that an investor plans to buy a CD in the amount of $1,000. Because the interest on the CD is compounded daily, the yearly interest rate is 5%, and hence there are 365 compounding periods in a year.
The annual percentage yield (APY) of the investment is computed as follows:
APY = [(1 + (0.05/365)) ^ 365] – 1 = 0.05127 or 5.127%
Even though the CD offered a rate of interest of 5%, the investor will end up receiving 5.127% of their initial investment owing to compound interest.
APR vs. APY for Interest Rate
If a loan has a lower annual percentage rate (APR), then the total amount of interest and fees that the borrower will have to pay back on the loan will also be reduced. This makes the loan more appealing to customers. On the other hand, when shopping for savings and investment products, investors will normally select assets that have higher APYs since they will achieve a bigger return on their investment. This is because investments with higher APYs pay interest at a higher rate.
APY vs. APR vs. EAR
One such method for calculating the cost of a loan or the return on an investment product is known as the effective annual rate or EAR. Since EAR takes into account compound interest, it is possible that it will provide more accurate results than APR in situations where the interest owing compounds at intervals other than yearly. Therefore, the EAR is a more accurate reflection of the “all-in” loan expenses that a borrower would incur.
Because they both take into account compound interest, EAR and APY are essentially interchangeable when discussing returns on investments.
Converting APR to APY
It is doable to change the APR into the APY. An annual percentage rate (APR) might be transformed into an annual percentage yield (APY) to gain a more accurate assessment of the total cost of a loan if the borrower was given both the APR and the rate at which the interest was compounded.
The following formula illustrates the relationship between APY and APR:
APY = [(1 + (APR/N)) ^ N] – 1
- N = the total number of times within a year that compounding occurs.
Let’s imagine a customer has a vehicle loan with an annual percentage rate (APR) of 4%, and the interest on the loan increases every day (365 compounding periods in a year).
The annual percentage yield for the customer’s auto loan would be:
APY = [(1 + (.04/365)) ^ 365] – 1 = 0.0408 or 4.08%
Key Takeaway: The annual percentage yield (APY) offers a more precise estimate of the cost of the loan than the annual percentage rate (APR) does since the APY takes into account the compounding of the interest on the loan.
Bottom Line
The Annual Percentage Rate (APR) is a metric that may be used by borrowers to evaluate various loan choices, while the Annual Percentage Yield (APY) is a metric that can be utilized by investors to compare When all other considerations are held constant, customers will typically choose loans with lower APRs, but investors would generally prefer investments with higher APYs.
