An amount of money at compound interest grows | vedclass

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Question

(A) 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

$2.5$

Vedclass · Answer

(A) 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.For $t = 4$ years,$3840 = P(1 + \frac{r}{100})^4$  --- $(i)$For $t = 5$ years,$3936 = P(1 + \frac{r}{100})^5$  --- (ii)Dividing equation (ii) by equation $(i)$:$\frac{3936}{3840} = \frac{P(1 + \frac{r}{100})^5}{P(1 + \frac{r}{100})^4}$$\frac{3936}{3840} = 1 + \frac{r}{100}$$\frac{3936}{3840} - 1 = \frac{r}{100}$$\frac{3936 - 3840}{3840} = \frac{r}{100}$$\frac{96}{3840} = \frac{r}{100}$$r = \frac{96 	imes 100}{3840} = \frac{9600}{3840} = 2.5$Therefore,the rate of interest is $2.5 \%$ per annum.

An amount of money at compound interest grows up to $Rs. 3840$ in $4$ $years$ and up to $Rs. 3936$ in $5$ $years$. Find the rate of interest (in $\%$)?

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