A sum of money at compound interest amounts t | vedclass

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

Vedclass · Accepted Answer

$6$

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(C) The formula for compound interest is $A = P(1 + \frac{R}{100})^T$,where $A$ is the amount,$P$ is the principal,$R$ is the rate of interest,and $T$ is the time in years.Given that the sum becomes thrice itself in $3$ years,we have $3P = P(1 + \frac{R}{100})^3$,which simplifies to $3 = (1 + \frac{R}{100})^3$.We want to find the time $T$ such that the sum becomes $9$ times itself,so $9P = P(1 + \frac{R}{100})^T$,which simplifies to $9 = (1 + \frac{R}{100})^T$.Since $9 = 3^2$,we can substitute the first equation into this: $9 = ((1 + \frac{R}{100})^3)^2 = (1 + \frac{R}{100})^6$.Comparing the exponents,we get $T = 6$ years.

$A$ sum of money at compound interest amounts to thrice itself in $3$ years. In how many years will it be $9$ times itself?

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