Approximately how long will it take an investment of $\$ 900$ to triple, if the interest rate is 3.75% per year compounded continuously?
A) $4.5 \text { years }$
B) $21 \text { years }$
C) $2.9 \text { years }$
D) $29 \text { years }$
E) $9 \text { years }$

Question

Quizplus · Accepted Answer

To find the time it takes for an investment to triple with continuous compounding, we use the formula $A = Pe^{rt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (decimal), and $t$ is the time the money is invested for in years. To triple the investment, $A = 3P$. Substituting the values and solving for $t$, we get $3 = e^{0.0375t}$. Taking the natural logarithm of both sides gives $ln(3) = 0.0375t$, and solving for $t$ gives $t = \frac{ln(3)}{0.0375} \approx 29$ years.

Approximately How Long Will It Take an Investment Of $900\$ 900$900

Approximately How Long Will It Take an Investment Of $\$ 900$