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# Annual Percentage Rate APR|Definition & Meaning

## Definition

The **annual interest** produced by a **sum** that is paid to investors or **charged** to borrowers is referred to as the **annual percentage rate (APR).** APR is a **percentage** that **expresses** the actual **annual** cost of **borrowing** money throughout the course of a loan or the **revenue** from an **investment.**

An **interest** rate is **written** as an **annual percentage** rate. It **factors** in **variables** like **monthly payments** to **determine** what proportion of the principal you’ll pay annually. The **annual percentage rate,** or APR, is the rate of interest **charged** on **investments** that are not adjusted for interest that has **accrued during** the year.

The interest rate and annual percentage rate can be easily understood with the help of the following graphs.

**Figure** -1 shows that Hales **borrows** 1000 dollars from a **bank** today and banks say that the **interest rate** is 10 **percent** over a year so **next year** He has to **1100 dollars** to the bank.

## How to Calculate the Annual Percentage Rate (APR)

The **annual percentage** **rate** (APR) is **determined** by multiplying the **interest** rate for **each** period by the total number of periods in a year to which the interest rate was **applied.** The number of times the rate is really **applied** to the **amount** is not stated. **Mathematically,** it is **calculated** as:

**APR = ((I + F/ P or LA) / N)) x 365 x 100**

Where I **represent** Interest which is the sum of all **installment payments** paid over the course of the loan. The P **represents** the amount a **person** really **borrows** is **known** as the principal. At the **conclusion** of the borrowing, they must repay it. N is the loan **term’s** daily count. Fees may be equal to other **costs, including transaction costs.**

## Different Types of Annual Percentage Rates

The two main types of **APR** are **fixed** and **variable.** A **fixed** APR does not change in reaction to changes in an index, in **contrast** to a variable APR. While this does not **guarantee** that **interest** rates will never change, it does mandate that the **issuer** give advance notice to the public. Variable **APRs** also referred to as **variable-rate APRs,** change in accordance with the index interest rate.

**APR** is typically a **decent** indicator of a loan’s cost. For instance, taking out a personal loan with high-interest rates can be **demanding.** If the loan is for a **sizable** sum, it is **best** to find out how much it would cost before deciding whether to accept it or not. This is due to the fact that in addition to the principal, the person **must** also pay the APR. **Sometimes** lenders will advertise low-interest rates to entice customers, but the additional fees may be quite taxing financially. This is **sometimes** especially true when it comes to **mortgage annual percentage** rates.

## Understanding the Annual Percentage Rate Graphically

The following figure visually explains the concept of the annual percentage rate.

Figure 2 **provides** a graphic **representation** of a 10-percent **interest** rate applied to a **$1,000** loan over the course of a **year.**

A **loan** of one thousand dollars with an **annual** interest rate of **twenty percent** is **graphically** represented in **figure 3**, which **shows** the **progression** of the loan over the **course** of **one year.**

Figure-4 shows the **graphical representation** of a**nnual percentage** rate where the **total tenure** is two year and loan **interest** are 700 dollars. The **annual percentage rate** in this case is **5.47 percent.**

## Numerical Examples for Annual Percentage Rate

### Example 1

**Consider** taking out a **$5,000** loan from a financial **institution** with a **two-year term** and a **simple** rate of **interest** of 5%. Over the **course** of the loan, you **would** pay $500 in interest. **However,** you were also **charged** a **$75** origination fee.

### Solution

The **loan’s** APR can be **calculated** in five steps:

**Fees** for origi**n**ation and total **interest charged** added together:

** 75 + 500 = 575 dollars**

Divide the answer from Step 1 from the **principle**, as appropriate:

**575 / 5,000 = 0.115**

**Divide** the **outcome** of **Step** two by the **number** of days **remaining** in the loan’s term:

**0.115 / 730 = 0.00015753**

Add **365** to the **result** from **Step** 3:

**0.00015753 x 365 = 0.0575**

To determine the APR **percentage,** multiply the Step 4 value by 100.

**0.575 x 100 = 5.75%**

Thus, the **annual percentage rate** is **5.75 percent.**

### Example 2

**Consider** Ali **taking** out a **$16,000** loan from a financial **institution** with a **two-year term** and a **simple** rate of **interest** of 16%. Over the **course** of the loan, you **would** pay **$1600** in interest. **However,** you were also **charged** a **$185** origination fee.

### Solution

The **loan’s** APR can be **calculated** in five steps:

**Fees** for origi**n**ation and total **interest charged** added together:

** 185 + 1600 = 1785 dollars**

Divide the answer from Step 1 from the **principle**, as appropriate:

**1785 / 16000 = 0.111**

**Divide** the **outcome** of **Step** two by the **number** of days **remaining** in the loan’s term:

**0.111 / 1095 = 0.000101**

Add **365** to the **result** from **Step** 3:

**0.000101 x 1095 = 0.110595**

To determine the APR **percentage,** multiply the Step 4 value by 100.

**0.110595 x 100 =11.05%**

Thus, the **annual percentage rate** is **11.05 percent.**

### Example 3

Think about **Amman** taking out a **$7,000** loan from a **bank** with a **two-year** term and a **7%** basic **interest** rate. You would pay interest on the **loan totaling** $700. You **have also assessed** an **origination** fee of **95 ****dollars,** however.

### Solution

The **loan’s** APR can be **calculated** in five steps:

**Fees** for origi**n**ation and total **interest charged** added together:

** 95 + 700 = 795 dollars**

Divide the answer from Step 1 from the **principle**, as appropriate:

**795 / 7000 = 0.11**

**Divide** the **outcome** of **Step** two by the **number** of days **remaining** in the loan’s term:

**0.11 / 730 = 0.00015**

Multiply **365** by the **result** from **Step** 3:

**0.00015 x 365 = 0.05475**

To determine the APR **percentage,** multiply the Step 4 value by 100.

**0.05475 x 100 = 5.47%**

Thus, the **annual percentage rate** is **5.47 percent.**

*All mathematical drawings and images were created with GeoGebra.*