If a bank charges a customer 15\% annual interest on a loan of \$10,000 compounded annually, what is the total interest earned by the bank after 3 years?

• A. \$4,000.00
• B. \$5,196.25
• C. \$5,225.00
• D. \$4,500.00

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the formula for compound interest. The formula is: \( A = P(1 + r)^t \), where \( A \) is the total amount after interest, \( P \) is the principal amount, \( r \) is the annual interest rate (in decimal form), and \( t \) is the time in years.
2. Step 2: Identify the values given in the problem. The principal amount \( P \) is \( \$10,000 \), the annual interest rate \( r \) is \( 15\% \) or \( 0.15 \) in decimal form, and the time \( t \) is 3 years.
3. Step 3: Substitute the values into the compound interest formula: \( A = 10,000(1 + 0.15)^3 \). This will calculate the total amount after 3 years, including the interest.
4. Step 4: To find the total interest earned by the bank, subtract the principal amount \( P \) from the total amount \( A \): \( \, \text{Interest} = A - P \).
5. Step 5: Perform the calculations step by step to determine \( A \) and then subtract \( P \) to find the total interest earned. Ensure all calculations are accurate and follow the order of operations.