Question

A sum of money placed at compound interest doubles itself in 4 years. In how many years will it amount to 8 times?
A.9 years
B.8 years
C.27 years
D.12 years

Answer 1

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So,
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$<b>Answer is 12 years.</b>$

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;
Thus, n = 12 years.

Answer 2

$\huge\boxed{\texttt{\fcolorbox{Red}{aqua}{Hey Mate!!!!}}}$

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Here is your answer.
A sum of money doubles itself in four years

Hence
Sum of money four times in eight years

Therefore
Sum of money 8 Times in 12 years

Option (D) 12 years is your answer
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