Raul deposited \$5,000 into a savings account that pays an annual interest rate of 6%, compounded annually. After 3 years, how much interest did Raul earn through compound interest in his savings account?

• A. \$1,200.00
• B. \$955.08
• C. \$1,000.00
• D. \$900.00

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. Here, \( P = 5000 \), \( r = 0.06 \) (since 6% = 0.06), and \( t = 3 \). Substitute these values into the formula.
3. Step 3: Calculate the total amount \( A \) after 3 years using the formula \( A = P(1 + r)^t \). This involves first adding \( 1 + r \), then raising the result to the power of \( t \), and finally multiplying by \( P \).
4. Step 4: Determine the compound interest earned by subtracting the principal \( P \) from the total amount \( A \). The formula for compound interest is \( ext{Interest} = A - P \).
5. Step 5: Compare the calculated interest to the options provided in the problem to identify the correct answer.