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Question

A sum of money doubles itself in 3 years at compound interest, when the interest is compounded annually.In how many years will the sum amount to 16 times of itself?
  1. 8 years
  2. 12 years
  3. 6 years
  4. 16 years


Solution

The correct option is B 12 years
The principal amount and the interest rate is same in both cases.
Therefore, 
2P=P(1+r100)n, here P is the principal, r is the rate of interest and n is the time period.
2=(1+r100)3
1+r100=213(1)

Assume the money becomes 16 times itself in n years.
16P=P(1+r100)n
1+r100=24n(2)
From(1)  and (2)
213=24n
13=4n
n=12 years

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