Question

a sum of money becomes eight times in 3 yrs. If the rate is compounded annually! in how much time will the same compound rate become sixteen times? ​

Answer 1

Answer:

4 years

Step-by-step explanation:

Let principal = P,

Then, amount received = 8P

Time = 3 years

A.C.Q,

A = P(1 + r/100)ⁿ

⇒ 8P = P(1 + r/100)³

⇒ 8 = (1 + r/100)³

⇒ (2)³ = (1 + r/100)³

⇒  2 = (1 + r/100)

⇒ r/100 = 1

⇒ r = 100%

Now, to get amount as 16 times of the principal,

⇒ 16P = P(1 + 100/100)^t

⇒ 2^t = 16

⇒ 2^t = 2⁴

⇒ t = 4

Therefore,

Time = 4 years

Hope it helps!