Annual Percentage Rate (APR) Calculator

How to Calculate Annual Percentage Rate (APR)

The Annual Percentage Rate (APR) is a crucial financial metric that represents the true cost of borrowing money. It includes not only the interest rate but also any additional fees associated with the loan. Understanding how to calculate APR is essential for consumers and financial professionals to make informed decisions about loans and credit offers.

APR Formula

The formula for calculating APR is:

$$\text{APR}=\left(\frac{\text{Total Cost of Loan}-\text{Principal}}{\text{Principal}}\right)\times \frac{365}{\text{Term in Days}}\times 100\mathrm{\%}$$

Where:

• Total Cost of Loan = Principal + Total Interest + Fees
• Principal = Loan Amount
• Term in Days = Loan Term in Months × 30

Calculation Steps

1. Calculate the monthly payment using the loan amount, interest rate, and term.
2. Determine the total amount paid over the life of the loan.
3. Calculate the total interest paid by subtracting the principal from the total amount paid.
4. Add any additional fees to the total interest to get the total cost of the loan.
5. Apply the APR formula to calculate the annual percentage rate.

Example Calculation

Let's calculate the APR for a loan with the following terms:

• Loan Amount: $10,000
• Loan Term: 36 months
• Interest Rate: 6% per year
• Additional Fees: $200

Step 1: Calculate monthly payment

$$\text{Monthly Payment}=\frac{10000\times (0.06/12)\times (1+0.06/12{)}^{36}}{(1+0.06/12{)}^{36}-1}=\$304.22$$

Step 2: Calculate total payments

$$\text{Total Payments}=\$304.22\times 36=\$10,951.92$$

Step 3: Calculate total interest

$$\text{Total Interest}=\$10,951.92-\$10,000=\$951.92$$

Step 4: Calculate total cost of loan

$$\text{Total Cost}=\$10,951.92+\$200=\$11,151.92$$

Step 5: Calculate APR

$$\text{APR}=\left(\frac{11151.92-10000}{10000}\right)\times \frac{365}{1080}\times 100\mathrm{\%}=7.31\mathrm{\%}$$

Therefore, the APR for this loan is 7.31%.

Visual Representation

This diagram illustrates the components of the loan and the APR. The blue section represents the principal amount, the green section shows the total interest, the red section indicates additional fees, and the purple dashed line represents the APR.