Katrina has invested some money for 12 years at a fixed interest rate that is compounded continuously. If her money will double in 8 years. will it triple in 12 years?

Question

rsadhvika · Answer

given that money will double in 8 years

$2 = e^{8r} \  => r = \frac{\ln 2}{8} ----- (1)$ 

need to check if it triples in 12 years
$3 = e^{12r} \  => r = \frac{\ln 3}{12} ----- (2)$ 

combining (1) and (2)

$\frac{\ln 2}{8}= \frac{\ln 3}{12} $ 

$\frac{\ln 2}{\ln 3}= \frac{8}{12} $ 

$\frac{\ln 2}{\ln 3}= \frac{2}{3} $ 

evaluate the log, if this true then the money will triple in 12 years