If a sum of money placed at compound interest | vedclass

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(C) Let the principal be $P = 1$ and the rate of interest be $R$ percent per annum.The formula for compound interest is $A = P(1 + \frac{R}{100})^T$.G

Vedclass · Accepted Answer

$15$

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(C) Let the principal be $P = 1$ and the rate of interest be $R$ percent per annum.The formula for compound interest is $A = P(1 + \frac{R}{100})^T$.Given that the money doubles in $5$ years,we have $2 = 1(1 + \frac{R}{100})^5$.We want to find the time $T$ such that the amount becomes $8$ times the principal,so $8 = 1(1 + \frac{R}{100})^T$.Since $8 = 2^3$,we can substitute the expression for $2$:$8 = (2)^3 = [(1 + \frac{R}{100})^5]^3$.Using the power rule $(a^m)^n = a^{m 	imes n}$,we get $8 = (1 + \frac{R}{100})^{5 	imes 3} = (1 + \frac{R}{100})^{15}$.Comparing this with $8 = (1 + \frac{R}{100})^T$,we find $T = 15$ years.

If a sum of money placed at compound interest,compounded annually,doubles itself in $5$ years,then the same amount of money will be $8$ times of itself in how many years?

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