Money triples in 15.50 years if it doubles in 10 years. Assume continuous compounding and rounding to two decimal places.

Question

Quizplus · Accepted Answer

Using the formula for continuous compounding, $A = P e^{rt}$, where $A$ is the amount 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 $r$ when the money doubles in 10 years. If money doubles, $A/P = 2$, so $2 = e^{10r}$. Solving for $r$ gives $r = \frac{\ln(2)}{10}$. To check if the money triples in 15.5 years, we substitute $r$ back into the formula with $t = 15.5$ and $A/P = 3$, resulting in $3 = e^{15.5(\ln(2)/10)}$. Evaluating this expression does not yield a true statement, indicating that the money does not exactly triple in 15.5 years under continuous compounding at the rate calculated.

Money Triples in 15