Suppose you deposit \$5,000 into a savings account that earns 6\% annual interest, compounded annually. What is the total balance in the account after 40 years?

• A. \$32,000.00
• B. \$51,429.50
• C. \$19,500.00
• D. \$48,000.00

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the formula for compound interest. The formula is: \( A = P \times (1 + r)^t \), where \( A \) is the total balance, \( P \) is the principal amount (initial deposit), \( r \) is the annual interest rate (in decimal form), and \( t \) is the number of years the money is invested or borrowed.
2. Step 2: Identify the values given in the problem. Here, \( P = 5000 \), \( r = 0.06 \) (6% annual interest rate converted to decimal), and \( t = 40 \) years.
3. Step 3: Substitute the values into the formula. The equation becomes: \( A = 5000 \times (1 + 0.06)^{40} \).
4. Step 4: Simplify the expression inside the parentheses first: \( 1 + 0.06 = 1.06 \). Then raise \( 1.06 \) to the power of \( 40 \).
5. Step 5: Multiply the result of \( 1.06^{40} \) by \( 5000 \) to calculate the total balance \( A \). This will give you the final amount in the savings account after 40 years.