Science:Math Exam Resources/Courses/MATH104/December 2016/Question 01 (b)/Solution 1

Following the hint, when we gain $8000, the total amount $A$ is $108,000. Substituting this with the annual interest rate converted into decimal form, $r=0.06$, into the continuously compounded interest formula:

$A=Pe^{rt},$

we get

$108000=100000e^{0.06t}.$

Then we divide by $100000$ on both sides and then take $\ln$ of both sides, to find $t$.

$1.08=e^{0.06t}\implies \ln 1.08=0.06t\implies t={\frac {\ln 1.08}{0.06}}$

Answer: $\color {blue}{\frac {\ln 1.08}{0.06}}$