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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