A sum of money at compound interest doubles i | vedclass

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Question

(A) The formula for compound interest is $A = P(1 + r/100)^n$,where $A$ is the amount,$P$ is the principal,$r$ is the rate,and $n$ is the time in year

Vedclass · Accepted Answer

$45$

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(A) The formula for compound interest is $A = P(1 + r/100)^n$,where $A$ is the amount,$P$ is the principal,$r$ is the rate,and $n$ is the time in years.Given that the sum doubles in $15$ years,we have $2P = P(1 + r/100)^{15}$,which simplifies to $2 = (1 + r/100)^{15}$.We want to find the time $n$ such that the sum becomes $8$ times itself,so $8P = P(1 + r/100)^n$,which simplifies to $8 = (1 + r/100)^n$.Since $8 = 2^3$,we can substitute $2$ with $(1 + r/100)^{15}$:$8 = ((1 + r/100)^{15})^3 = (1 + r/100)^{45}$.Comparing the exponents,we get $n = 45$ years.Thus,the sum becomes $8$ times itself in $45$ years.

$A$ sum of money at compound interest doubles itself in $15$ years. It will become eight times of itself in (in $years$):

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