Question

compound interest if a certain sum of money Doubles in n year then the amount will be four fold in ​

Answer 1

Question : At compound interest, if a certain sum of money doubles in 'n' year then the amount will be four fold in

$\fbox{ANSWER} \\\\Let\ the\ principal\ be\ Rs.x \\\\ Then,\ amount\ will\ be\ Rs. 2x \\\\ Time=n\ years \\\\ \therefore x\bigg(1+\frac{R}{100}\bigg)^n = 2x \\\\ \implies \bigg(1+\frac{R}{100}\bigg)^n = 2 \\\\ Let\ it\ become\ four\ fold\ in\ N\ years, \\\\ Than,\ x\bigg(1+\frac{R}{100}\bigg)^N = 4x \\\\ \implies \bigg(1+\frac{R}{100}\bigg)^N = 4 \\\\ \implies 2^2=\bigg(1+\frac{R}{100}\bigg)^N \\\\ \implies \bigg(1+\frac{R}{100}\bigg)^2^n=\bigg(1+\frac{R}{100}\bigg)^N \\\\ \therefore N=\fbox{2n\ years.}$

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