Approximately how many years are required for a sum of money to double at 4% annual compound interest?

Approximately how many years are required for a sum of money to double at 4% annual compound interest?

• A. 16 years
• B. 14 years
• C. 20 years
• D. 17.7 years

Answer: (D)

At this rate, the money grows by a factor of 1.04 each year, so doubling means solving (1.04)^t = 2. Take logs to isolate t: t = ln(2) / ln(1.04). Using common approximations, ln(2) ≈ 0.6931 and ln(1.04) ≈ 0.03922, so t ≈ 0.6931 / 0.03922 ≈ 17.7 years. This is the precise time it takes for the amount to double with 4% annual compound interest. As a quick check, the Rule of 72 gives about 72/4 = 18 years, which is a close but slightly rough estimate; the exact calculation yields 17.7 years.

At this rate, the money grows by a factor of 1.04 each year, so doubling means solving (1.04)^t = 2. Take logs to isolate t: t = ln(2) / ln(1.04). Using common approximations, ln(2) ≈ 0.6931 and ln(1.04) ≈ 0.03922, so t ≈ 0.6931 / 0.03922 ≈ 17.7 years. This is the precise time it takes for the amount to double with 4% annual compound interest. As a quick check, the Rule of 72 gives about 72/4 = 18 years, which is a close but slightly rough estimate; the exact calculation yields 17.7 years.