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A sum of money deposited at compound interest doubles itself in 4 years. It will amount to sixteen times at the same rate in
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Explanation:
Let sum = Rs.100, time = 4 years,
Amount due in 4 years = Rs.200
Therefore, 100=(1+R\100)^4=200
= (1+R\100)^4=2
= (1+R\100)=2 1\4 …(i)
Let the amount becomes 16 times in n years
Therefore, 100(1+R\100)^n=1600 …(ii)
= (1+R\100)^n=16
From equations (i) and (ii)
(2 1\4)^n=16=2^4
=>n\4=4
=> n = 16