The money invested in a company is compounded | vedclass

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Question

(B) For continuous compounding,the formula is $A = Pe^{rt}$.Given $P = 400$,$A = 800$ at $t = 6$ years.$800 = 400e^{6r} \implies e^{6r} = 2 \implies 6

Vedclass · Accepted Answer

₹ $18101.76$

Vedclass · Answer

(B) For continuous compounding,the formula is $A = Pe^{rt}$.Given $P = 400$,$A = 800$ at $t = 6$ years.$800 = 400e^{6r} \implies e^{6r} = 2 \implies 6r = \ln(2) \implies r = \frac{\ln(2)}{6}$.We need to find the amount $A$ at $t = 33$ years.$A = 400e^{33r} = 400e^{33 	imes \frac{\ln(2)}{6}} = 400e^{5.5 \ln(2)} = 400(e^{\ln(2)})^{5.5} = 400(2^{5.5})$.$2^{5.5} = 2^5 	imes 2^{0.5} = 32 	imes \sqrt{2}$.Given $\sqrt{2} \approx 1.4142$,so $2^{5.5} = 32 	imes 1.4142 = 45.2544$.$A = 400 	imes 45.2544 = 18101.76$.Thus,the amount at the end of $33$ years is ₹ $18101.76$.

The money invested in a company is compounded continuously. ₹ $400$ invested today becomes ₹ $800$ in $6$ years. What will it become at the end of $33$ years? (Given $\sqrt{2} \approx 1.4142$)

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