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In how much time rs. 6400 will amount Rs...

In how much time rs. 6400 will amount Rs. 6561 at the rate of 5% compound interest when interest is compounded quaterly?

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Let the required tiem `=n` years
As per question `Rs. 6400(1+(5/4)/100)^(4n)=Rs. 6561`
Or `(1+1/80)^(4n)=6561/6400` or `(81/80)^(4n)=6561/6400`
or `(81/80)^(4n)=(81/80)^(2)`
`implies4n=2impliesn=2/4=2/4xx12` months `=6` months
Hence the required time `=6` months.
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