A sum of money lent at compound interest amou | vedclass

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(D) Let the principal amount be $P$ and the rate of interest be $r \%$ per annum.The formula for the amount $A$ after $n$ years at compound interest i

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$10$

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(D) Let the principal amount be $P$ and the rate of interest be $r \%$ per annum.The formula for the amount $A$ after $n$ years at compound interest is $A = P(1 + \frac{r}{100})^n$.According to the problem:For $n = 2$ years,$P(1 + \frac{r}{100})^2 = 1460$  --- (Equation $1$)For $n = 3$ years,$P(1 + \frac{r}{100})^3 = 1606$  --- (Equation $2$)Dividing Equation $2$ by Equation $1$:$\frac{P(1 + \frac{r}{100})^3}{P(1 + \frac{r}{100})^2} = \frac{1606}{1460}$$1 + \frac{r}{100} = \frac{1606}{1460}$$1 + \frac{r}{100} = 1.1$$\frac{r}{100} = 1.1 - 1 = 0.1$$r = 0.1 	imes 100 = 10 \%$Thus,the rate of interest is $10 \%$ per annum.

$A$ sum of money lent at compound interest amounts to ₹ $1460$ in $2$ years and to ₹ $1606$ in $3$ years. The rate of interest (in $\%$) per annum is:

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