Before investing money in a high-yield cash account, such as a CD, or applying for a personal loan, credit card, or mortgage, it is crucial to understand the essential concepts of annual percentage rate (APR) and annual percentage yield (APY).
However, APR and APY may sound similar as they’re involved in calculating the interests, but they are entirely different. For instance, in APR, the interest amount is paid to the lender for lending the loan, whereas in APY, the interest amount is earned by the investor for investing in a high-yield account.
In this article, you’ll find a detailed view that explains APY vs APR and how interests are calculated using these concepts.
What Is APR?
The annual percentage rate is the yearly amount the borrower must pay to obtain the loan. Remember, this amount is not considered a part of the original amount lent as a loan.
Usually, this cost comes under general interest or other fees like maintenance fees, loan grant fees, etc. However, there are a few lenders who consider APR and these additional fees as separate costs.
APR Vs Interest Rates
As discussed, APR is the cost paid to borrow a loan from the lender, which may include other miscellaneous fees. In contrast, interest rates are the cost expressed in percentage for the loan borrowed, and this cost does not include any additional fees.
According to the Consumer Financial Protection Bureau (CFPB), APR is the cost of borrowing and may vary depending upon the type of loan, i.e., personal, car, mortgage, etc. At the same time, the interest rate is the cost ONLY for the principal amount lent as a loan. This is one of the significant reasons why APR is higher when compared to the interest rate.
How To Calculate APR?
To calculate APR, consider the principal amount, the loan tenure period in days, and the extra charges implied.
The formula to calculate APR is:
APR = ((Interest + Fees / Loan amount) / Number of days in loan term)) x 365 x 100
To substitute the value in the given formula, follow these steps –
- Calculate the interest rate using a simple interest formula, i.e., (PxRxT)/100
- Add the extra charges to the interest calculated in Step 1.
- Divide the above-calculated value by the principal amount.
- Followed by step 3, divide by the total number of days in loan tenure.
- Multiply all the above by 1, i.e., 365 days.
- Multiply the value obtained from the above calculation by 100 to get APR.
For Example
Consider the case of Ajay, who borrows ₹2,000 with a 5% interest rate for two years. Alongside the loan, there is a closing administrative cost of ₹200. To determine the APR, we begin by calculating the Interest using the simple interest formula:
A= P×(1+RxT)
Where:
- A is the total accrued amount,
- P is the principal amount,
- R is the interest rate, and
- T is the period.
Given that P = ₹2,000, R=5%, and T=2 years, the calculation is A=2000×(1+0.05×2), resulting in A = ₹2,200.
The interest accrued is A – P = ₹2,200 – ₹2,000 = ₹200.
We use the APR formula to add this Interest to the closing cost: Administrative Cost + Interest = ₹200 + ₹200 = ₹400.
Finally, to determine the APR percentage, divide the total by the loan amount, then multiply by 100:
APR=(400/2000)÷2×1×100=10%
This means that the APR for this loan is 10%. Notably, despite the apparent 5% interest rate, the actual annual cost of the loan, including all charges, is 10%.
What Is APY?
The APY measures the annualised rate of return that investors can anticipate from interest-bearing accounts like Certificates of Deposit (CDs), Individual Retirement Accounts (IRAs), or high-yield cash accounts. Financial institutions, including banks, express APY as a percentage to determine the annual interest earnings.
By Truth in Savings regulations, financial institutions must furnish investors with APY details before the account opening. This information empowers you to compare various investment options, aiding in the decision-making process for adding specific accounts to your investment portfolio.
Unlike simple interest, APY incorporates compound interest. This means the financial institution calculates earned interest annually, adding it to your current balance. Generally, a higher APY indicates a more favourable rate of return on your investment.
APY Vs Interest Rates
APY is more concentrated on the interest an investor owes for the deposit annually. APY is calculated based on compound interest, i.e., an investor not only earns interest for the amount deposited in the high-yield or any other account but also earns an additional interest on the interest already earned.
When comparing APR with interest rates, interest rates are just the cost calculated in percentage for the principal amount deposited in the account. At the same time, APR measures more than just an interest rate.
How To Calculate APY?
The formula to calculate APY: (1+r/n)^n-1
Where ‘r’ is the interest rate and ‘n’ is the number of times the interest is compounded yearly.
Follow the steps given below to calculate APY using the formula –
- Convert the interest rate into decimals. For example, if the interest rate is 5%, the conversion is r= 0.05.
- Determine the number of years that the interest has been compounded ‘n,’ e.g., an interest is compounded annually (1), semi-annually (2), quarterly (4), monthly (12), or daily (365).
- Substitute all the values in the formula – (1+r/n)^n-1
For Example:
Let’s say you deposit ₹1,000 in a savings account with an annual interest rate of 2% compounded monthly. Here’s how to calculate the APY:
Determine the period rate:
- Divide the annual rate by the number of compounding periods. In this case, there are 12 months in a year, so the period rate is 2% / 12 = 0.167%.
Apply the formula:
- Use the formula APY = (1 + r/n)^n – 1, where r is the period rate and n is the number of compounding periods.
- Plug in the values: APY = (1 + 0.00167)^12 – 1
- Calculate: APY = 1.0205^12 – 1 = 1.02509 – 1
- Multiply by 100 to convert to a percentage: APY = 0.02509 * 100 = 2.509%
Therefore, the APY for this account is 2.509%, which is slightly higher than the stated annual interest rate of 2%. This is because of the effect of compounding, where the interest is earned not only on the initial deposit but also on the accumulated interest from previous periods.
What Is The Difference Between APY And APR?
Wondering what is the difference between APR and APY? The difference lies in factors like the purpose, fees and extra charges, type of account, i.e., investment or credit, and the method of interest calculations.
Let us discuss each factor in detail –
- Purpose: This is the noticeable difference that a person needs to know to proceed with a loan application or look for an investment plan. Here, APR is the rate of interest calculated for the loan amount lent by the financial institution, and APY is the interest rate of return for an investment annually.
- Fees and extra charges: In the case of APR, the lender who lends money can add additional fees like maintenance, loan tenure fees, etc, along with the interest amount. While minimal or no such additional charges are added upon APY, this purely involves compounding the interest rate according to the time, i.e., annual or semi-annual.
- Type of account: This is the basic difference between APR and APY. APR deals with credit and loan accounts, whereas APY involves investment and high-yield saving accounts.
With all these points, calculating the rate of interest is the critical difference between APR and APY.
APR VS APY Example
Assume you have taken a loan of ₹4,000 with an APR of 4%. Interest compounds monthly, and the loan term is 1 year, i.e., 12 payments, so you’ll repay roughly ₹340.60 monthly. Over one year, you’ll repay ₹87.20 in interest.
In contrast, assume investing ₹4,000 into a 12-month CD with 4% APY. It compounds monthly. At the end of the year, you’ll earn ₹162.97 if you keep all of the CD’s funds during the year.
There is a capital gain in APY when you pay more than the amount lent as a loan in APR. Financial institutions provide different schemes when applying for a loan based on the amount borrowed, period, and other factors. Look for a lower APR to pay less interest.
On the other hand, if you’re looking to invest in any CDs, choose an account type with a higher APY since the amount keeps compounding and your earnings are increased.
Conclusion
Navigating the worlds of borrowing and investing requires understanding the concept of APY vs APR. The annual percentage rate, or APR, includes all fees and interest rates that are significant when applying for loans. It’s all about cutting expenses and going for cheaper rates.
Conversely, APY excels in investing by demonstrating prospective profits through compound interest. Here, the primary goals are maximising profits and pursuing better rates for deposited funds.
The leading cause of their discrepancy is the interest computation methods—complex vs simple. Knowing these ideas helps you make wise decisions, whether choosing an investment or obtaining a loan. A higher APY increases returns, while a lower APR reduces repayment.
Frequently Asked Questions
Which Is Better, APR Or Interest Rates?
Interest rates are better than APR because the person lending the loan adds up all the miscellaneous fees, whereas the interest rates are the amount expressed in percentage only from the loan borrowed. Therefore, the interest rate is lower and better compared to APR.
Which Is Profitable Between APR And APY?
APY is profitable because a person invests in a high-yield savings account, and the rate of return is compounded annually; they earn interest for the money they have deposited and not withdrawn in a year. Meanwhile, APR is interest paid to the loan amount borrowed, which is an extra cost.
What Are APR And APY In Crypto?
APR in cryptocurrencies reflects interest earned or paid on assets through activities like yield farming, lending, or staking annually, without compounding. In contrast, APY includes compounding effects, showcasing total interest over 12 months. These metrics are vital for evaluating rewards and returns in the dynamic cryptocurrency finance realm, emphasising true growth potential with earnings reinvestment.
What Is The Difference Between Simple And Compound Interest?
Simple interest (SI) is calculated for the principal amount for a given time – in the case of APR calculation (SI) is considered for the loan amount borrowed. In comparison, compound interest (CI) is calculated for the principal amount and the interest from the previous period. In the case of APY calculation, CI is considered for the amount invested.
