Question

How long does it take for $1700 to double if it is invested at 9 % compounded continuously? Round your answer to two decimal places.Answer How to enter your answer (opens in new window) 5 PointsKeypadKeyboard Shortcutsyears

Answer 1

Solution:

Given:

$\begin{gathered} P=\text{ \ }1700 \\ r=9\text{ \%}=\frac{9}{100}=0.09 \\ For\text{ the amount to double,} \\ A=2P \\ A=2\times1700=3400 \\ A=\text{ \ }3400 \end{gathered}$

Using the compound interest formula;

$\begin{gathered} A=P(1+r)^t \\ 3400=1700(1+0.09)^t \\ \frac{3400}{1700}=(1+0.09)^t \\ 2=1.09^t \\ \\ To\text{ solve for the time, take the logarithm of both sides} \end{gathered}$

Taking the logarithm of both sides;

$\begin{gathered} log2=log1.09^t \\ \\ Applying\text{ the law of logarithm,} \\ loga^x=xloga \\ \\ The\text{ equation becomes;} \\ log2=t\text{ }log1.09 \\ Hence, \\ \frac{log2}{log1.09}=t \\ t=8.04\text{ years} \end{gathered}$

Therefore, it will take approximately 8.04 years to double the initial $1700.