A sum of money place at compound interest doubles itself in 4 years. In how many years will it amount to eight times itself ?

A. 16

B. 8

C. 12

D. 20

Answer : C. 12…

Explanation :

Let, Principal = Rs. 100.
Amount = Rs. 200.
Rate = r%
Time = 4 years.

Now,
A = P * [ 1 + (r/100) ]n
200 = 100 * [ 1 + (r/100) ]4
2 = [1 + (r/100)]4 ……….. (i)
If sum become 8 times in the time n years, then,
8 = ( 1 + (r/100) )n
23 = ( 1 + (r/100) )n …….. (ii)

Using eqn (i) in (ii), we get
( [1 + (r/100) ]4)3 = ( 1 + (r/100) )n
[1 + (r/100)]12 = (1 + (r/100))n
n = 12 years.

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