An amount of money at compound interest grows | vedclass

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

Vedclass · Accepted Answer

$2.5$

Vedclass · Answer

(A) The formula for the amount $A$ at compound interest is given by $A = P(1 + \frac{R}{100})^T$,where $P$ is the principal,$R$ is the rate of interest,and $T$ is the time in years.For $T = 4$ years,$A_4 = P(1 + \frac{R}{100})^4 = 3840$  --- (Equation $1$)For $T = 5$ years,$A_5 = P(1 + \frac{R}{100})^5 = 3936$  --- (Equation $2$)Dividing Equation $2$ by Equation $1$:$\frac{P(1 + \frac{R}{100})^5}{P(1 + \frac{R}{100})^4} = \frac{3936}{3840}$$1 + \frac{R}{100} = \frac{3936}{3840}$$\frac{R}{100} = \frac{3936}{3840} - 1$$\frac{R}{100} = \frac{3936 - 3840}{3840} = \frac{96}{3840}$$R = \frac{96}{3840} 	imes 100 = \frac{9600}{3840} = 2.5 \%$Thus,the rate of interest is $2.5 \%$.

An amount of money at compound interest grows up to ₹ $3,840$ in $4$ years and up to ₹ $3,936$ in $5$ years. Find the rate of interest (in $\%$).

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