A $10,000 investment at a 10% return will take approximately how many years to be worth $20,000?

A $10,000 investment at a 10% return will take approximately how many years to be worth $20,000?

• A. 7
• B. 5
• C. 10
• D. 12

Answer: (A)

With compound growth, the value after n years is the initial amount times (1 plus the annual return) raised to n. Here that’s 10,000 × (1.10)^n, and we want it to reach 20,000, so (1.10)^n = 2. Solve by taking logarithms: n = ln(2) / ln(1.10) ≈ 0.6931 / 0.0953 ≈ 7.3. So it takes a little over seven years to double. A quick rule of thumb, the Rule of 72, also gives about 72/10 ≈ 7.2 years, which matches. Therefore about seven years is the right ballpark.

With compound growth, the value after n years is the initial amount times (1 plus the annual return) raised to n. Here that’s 10,000 × (1.10)^n, and we want it to reach 20,000, so (1.10)^n = 2. Solve by taking logarithms: n = ln(2) / ln(1.10) ≈ 0.6931 / 0.0953 ≈ 7.3. So it takes a little over seven years to double. A quick rule of thumb, the Rule of 72, also gives about 72/10 ≈ 7.2 years, which matches. Therefore about seven years is the right ballpark.