#color(red)("You have not stated the number of years.")#

#color(red)("The use of the word 'annually' implies more than 1 year")#

Let the number of years be #n#

#" "$144(1+x/100)^n=$414#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Suppose the number of years is 1 then")#

#" "144+(144xx ?/100)=414#

#color(brown)("Subtract 144 from both sides")#

#" "144xx ?/100=270#

#color(brown)("Multiply both sides by "100/144)#

#color(blue)(" "?%=270xx100/144 = 187.5%)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Suppose "n>1)color(magenta)(" "->" Needs algebra")#

#color(brown)("Notice that " (1+x/100) ->((100+x)/100))#

#color(brown)("Taking logs of both sides")#

#" "log($144)+nlog((100+x)/100)=log($414)#

#" "nlog((100+x)/100)=log(414)-log(144)#

#" "log((100+x)/100)=(log(414)-log(144))/n#

#" "log(100+x)-log(100)=(log(414)-log(144))/n#

#" "log(100+x)=(log(414)-log(144))/n + log(100)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(brown)("But "log(100)=2#

#" "log(100+x)=(log(414)-log(144))/n + 2#

#" "100+x=log^(-1)((log(414)-log(144))/n + 2)#

#" "color(blue)(x%=log^(-1)((log(414)-log(144))/n + 2) - 100)#