The money invested in a company is compounded | vedclass

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(B) For continuous compounding,the amount $A$ at time $t$ is given by the formula $A(t) = P e^{rt}$,where $P$ is the principal amount,$r$ is the rate

Vedclass · Accepted Answer

$12800$

Vedclass · Answer

(B) For continuous compounding,the amount $A$ at time $t$ is given by the formula $A(t) = P e^{rt}$,where $P$ is the principal amount,$r$ is the rate of interest,and $t$ is the time in years.Given $P = 400$ and $A(6) = 800$,we have $800 = 400 e^{6r}$.Dividing by $400$,we get $2 = e^{6r}$.Taking the natural logarithm on both sides,$\ln(2) = 6r$,so $r = \frac{\ln(2)}{6}$.We need to find the amount at $t = 30$ years: $A(30) = 400 e^{30r}$.Substituting $r = \frac{\ln(2)}{6}$,we get $A(30) = 400 e^{30 	imes \frac{\ln(2)}{6}} = 400 e^{5 \ln(2)}$.Using the property $e^{a \ln(b)} = b^a$,we get $A(30) = 400 	imes 2^5$.$A(30) = 400 	imes 32 = 12800$.Thus,the amount at the end of $30$ years will be ₹ $12800$.

The money invested in a company is compounded continuously. If ₹ $400$ invested today becomes ₹ $800$ in $6$ years,then at the end of $30$ years,it will become (in ₹)

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