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Question

A sum of money invested at compound interest doubles itself in six years. In how many years will it become 64 times itself at the same rate of compound interest?

A
30
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B
36
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C
42
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D
48
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Solution

The correct option is B 36
When interest is compounded, Amount A=P(1+R100)n
Given, 2P=P(1+R100)6
=>2=(1+R100)6 --- (1)
And, 64P=P(1+R100)n
=>64=(1+R100)n
=>26=(1+R100)n
From eqn 1
=>((1+R100)6)6=(1+R100)n
=>(1+R100)36=(1+R100)n
=>n=36

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