Question

in how much time will a certain sum be 1.5 times the principal at 10% per annum

Answer 1

(1) B = P(1+r)^t or
(2) B/P = (1+r)^t
The problem statement has 
(3) B/P = 1.5 and
(4) r = 10% or 
(5) r = 0.10
Then we have
(6) 1.5 = (1 + 0.10)^t or

(7) 1.5 = (1.1)^t
Now take the log or ln of both sides to get
(8) ln(1.5) = t*ln(1.1) or
(9) t = ln(1.5)/ln(1.1)
Use a scientific calculator to evaluate (9), and get
(10) t = 0.405/0.0953 or
(11) t = 4.25416...
Use (7) to check the value of t
Is (1.5 = (1.1)^4.254..)?
Is (1.5 = 1.5)? Yes
Answer: It will take 4.25... years for the principal P to "grow" to 1.5 times P.