Answer is:
Given A=96000, P=67785 and r = 8.7%
We know that, continuous compound interest formula is A = Pe^(rt)
where
P = principal amount
r = annual interest rate
t = years
A = amount after t
Now
Use A = Pe^(rt) with A=96000, P=67785 and r = 0.087
Therefore, 96000 = 67785 e^(0.087 t)
96000/ 67785 = e^(0.087 t)
1.42 = e^(0.087 t)
log (1.42) = 0.087 t
0.351 = 0.087 t
t = 0.351/0.087
t = 4.034
There are many methods to solve the simple interest, compound interest and continuous compound interest this was the one method which i solved for you.