A sum of money becomes eight times in 3 years, if the rate is compounded annually. In how much time will the same amount at the same compound rate become sixteen times?

Explanation:

Let principal = P,

Case (1): Time = 3 years,

Amount = 8P

8P=P(1+R\100)^3

(2)3=(1+R\100)^3

Taking cube root of both sides

2=(1+R\100)

R=100 %

Case 2: Let after t years it will be 16 times

16P=P(1+R\100)^t

16=(2)^t

(2)4=(2)^t

t = 4 years

Hence Required time (t) = 4 years