A sum of money placed at compound interest do | vedclass

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(D) Let the initial principal be $P$.According to the compound interest formula,the amount $A$ after $n$ years is given by $A = P(1 + r/100)^n$.Given

Vedclass · Accepted Answer

$15$

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(D) Let the initial principal be $P$.According to the compound interest formula,the amount $A$ after $n$ years is given by $A = P(1 + r/100)^n$.Given that the sum doubles in $5$ years,we have $2P = P(1 + r/100)^5$,which implies $(1 + r/100)^5 = 2$.We want to find the time $t$ such that the amount becomes $8P$.So,$8P = P(1 + r/100)^t$,which simplifies to $8 = (1 + r/100)^t$.Since $8 = 2^3$,we can substitute $2$ with $(1 + r/100)^5$:$8 = ((1 + r/100)^5)^3 = (1 + r/100)^{15}$.Comparing the exponents,we get $t = 15$ years.Therefore,the sum will become $8$ times itself in $15$ years.

$A$ sum of money placed at compound interest doubles itself in $5$ years. It will amount to eight times itself at the same rate of interest in (in $years$):

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