A sum of money placed at compound interest do | vedclass

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(C) The formula for compound interest is $A = P(1 + \frac{R}{100})^n$, where $A$ is the amount, $P$ is the principal, $R$ is the rate, and $n$ is the

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$15$

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(C) The formula for compound interest is $A = P(1 + \frac{R}{100})^n$, 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 $5 \, 	ext{years}$, we have $2P = P(1 + \frac{R}{100})^5$, which simplifies to $(1 + \frac{R}{100})^5 = 2$.We want to find the time $N$ such that the sum becomes $8$ times itself: $8P = P(1 + \frac{R}{100})^N$.This simplifies to $(1 + \frac{R}{100})^N = 8$.Since $8 = 2^3$, we can substitute $2 = (1 + \frac{R}{100})^5$ into the equation:$(1 + \frac{R}{100})^N = [(1 + \frac{R}{100})^5]^3$.$(1 + \frac{R}{100})^N = (1 + \frac{R}{100})^{15}$.Comparing the exponents, we get $N = 15 \, 	ext{years}$.

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

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