Question #a2c15

1 Answer
May 23, 2017

Answer:

After #9.327 (3dp)# years both amount will be same.

Explanation:

Let both amount will be same after #t# years.
Formula for continuously compounded interest is # A=P*e^(r/100*t)#
Wherte r = rate of interest , P=Principal , t is number of years.

At Bob's Bank # r=12% :' r/100=12/100=0.12 , P=4000#

At Charlie's Bank # r=6% :' r/100=6/100=0.06 , P=7000#

after #t# years #A_b=A_c :. 4000*e^(0.12t)=7000*e(0.06t)# or
#(e^(0.12t))/(e(0.06t)) = 7000/4000=7/4 # Or

#e^((0.12-0.06)t) = 1.75 or e^(0.06t) =1.75 # Taking #ln# on both sides we get, #0.06t *ln(e) =ln(1.75) or 0.06t = 0.5596; [ln(e)=1]# or

#t ~~ 0.5596/0.06 =9.327 (3dp)# years [Ans]