If money is compounded continuously, it will double in about 6.3 years if it triples in 10 years.

Question

Quizplus · Accepted Answer

Using the formula for continuous compounding, $A = Pe^{rt}$, where $A$ is the amount of money after time $t$, $P$ is the principal amount, $r$ is the rate, and $e$ is the base of the natural logarithm (approximately 2.71828), we can find the rate $r$ that triples the money in 10 years ($A/P = 3$) and then use that rate to find the time it takes to double ($A/P = 2$). Solving for $r$ in $3 = e^{r*10}$ gives $r \approx 0.10986$. Plugging this rate into $2 = e^{r*t}$ to solve for $t$ gives $t \approx 6.3$ years.

If Money Is Compounded Continuously, It Will Double in About