About how many years does it take for money to double when compounded continuously at 4% per year?
A) 35
B) 9
C) 18
D) 17

Question

Quizplus · Accepted Answer

The formula for continuous compounding is $A = P e^{rt}$, where $A$ is the amount of money after time $t$, $P$ is the principal amount, $r$ is the annual interest rate, and $e$ is the base of the natural logarithm. To double the money, $A/P = 2$, so $2 = e^{0.04t}$. Taking the natural logarithm of both sides gives $ln(2) = 0.04t$, and solving for $t$ gives $t = \frac{ln(2)}{0.04} \approx 17.33$ years, which rounds to 17 years.

About How Many Years Does It Take for Money to Double