What annual interest rate, compounded annually, will cause your money to double in four years?

• A. 25.00\%
• B. 18.92\%
• C. 8.00\%
• D. 12.50\%

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the problem. You are tasked with finding the annual interest rate, compounded annually, that will cause an initial investment to double in four years. This involves using the formula for compound interest.
2. Step 2: Recall the formula for compound interest: \( A = P(1 + r)^t \), where \( A \) is the future value, \( P \) is the principal amount, \( r \) is the annual interest rate, and \( t \) is the time in years. In this case, \( A \) is twice \( P \), and \( t \) is 4 years.
3. Step 3: Substitute the known values into the formula. Since \( A = 2P \), the equation becomes \( 2P = P(1 + r)^4 \). Simplify by dividing both sides by \( P \), resulting in \( 2 = (1 + r)^4 \).
4. Step 4: Solve for \( r \). Take the fourth root of both sides to isolate \( 1 + r \): \( \sqrt[4]{2} = 1 + r \). Then subtract 1 from both sides to find \( r \): \( r = \sqrt[4]{2} - 1 \).
5. Step 5: Convert \( r \) into a percentage by multiplying by 100. This will give you the annual interest rate that causes the money to double in four years.