A certain sum of money at compound interest g | vedclass

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(C) Let the principal be $P$ and the rate of interest be $R \%$ per annum.For compound interest,the amount $A$ after $n$ years is given by $A = P(1 +

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$1 \frac{2}{3} \%$

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(C) Let the principal be $P$ and the rate of interest be $R \%$ per annum.For compound interest,the amount $A$ after $n$ years is given by $A = P(1 + R/100)^n$.Given:Amount after $2$ years $(A_2)$ = $P(1 + R/100)^2 = 12960$  --- (Equation $1$)Amount after $3$ years $(A_3)$ = $P(1 + R/100)^3 = 13176$  --- (Equation $2$)Dividing Equation $2$ by Equation $1$:$\frac{P(1 + R/100)^3}{P(1 + R/100)^2} = \frac{13176}{12960}$$(1 + R/100) = \frac{13176}{12960}$$R/100 = \frac{13176}{12960} - 1$$R/100 = \frac{13176 - 12960}{12960} = \frac{216}{12960}$$R = \frac{216}{12960} 	imes 100 = \frac{2160}{129.6} = \frac{21600}{1296} = \frac{50}{3} \% = 16.66 \%$Wait,checking the calculation: $\frac{216}{12960} = \frac{1}{60}$.$R = \frac{1}{60} 	imes 100 = \frac{10}{6} = \frac{5}{3} = 1 \frac{2}{3} \%$.Therefore,the correct option is $C$.

$A$ certain sum of money at compound interest grows up to ₹ $12960$ in $2$ years and up to ₹ $13176$ in $3$ years. Find the rate per cent per annum.

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