In a bank,the principal increases continuousl | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $P$ be the principal at time $t$.Given that the principal increases continuously at the rate of $5 \%$ per year,we have the differential equat

Vedclass · Accepted Answer

$Rs. 1648$

Vedclass · Answer

(A) Let $P$ be the principal at time $t$.Given that the principal increases continuously at the rate of $5 \%$ per year,we have the differential equation:$\frac{dP}{dt} = \frac{5}{100} P = 0.05 P$Separating the variables,we get:$\frac{dP}{P} = 0.05 dt$Integrating both sides:$\int \frac{dP}{P} = \int 0.05 dt$$\ln P = 0.05 t + C$$P = e^{0.05 t + C} = e^C \cdot e^{0.05 t}$Let $P_0 = e^C$ be the initial principal at $t = 0$. Given $P_0 = 1000$,so $P = 1000 e^{0.05 t}$.For $t = 10$ years:$P = 1000 e^{0.05 	imes 10} = 1000 e^{0.5}$Using the given value $e^{0.5} = 1.648$:$P = 1000 	imes 1.648 = 1648$Thus,the amount after $10$ years will be $Rs. 1648$.

In a bank,the principal increases continuously at the rate of $5 \%$ per year. An amount of $Rs. 1000$ is deposited in this bank. How much will it be worth after $10$ years? (Given: $e^{0.5} = 1.648$)

Similar Questions

In a certain culture of bacteria,the rate of increase is proportional to the number of bacteria present at that instant. It is found that there are $10,000$ bacteria at the end of $3$ hours and $40,000$ bacteria at the end of $5$ hours. Find the number of bacteria present in the beginning.

If the surrounding air is kept at $25^{\circ} C$ and a body cools from $80^{\circ} C$ to $50^{\circ} C$ in $30 \text{ minutes}$,then the temperature of the body after one hour will be

The differential equation of displacement of all $Simple \ Harmonic \ Motions$ of given period $T = 2\pi / n$ is:

The differential equation $\frac{dy}{dx} = \frac{\sqrt{1-y^2}}{y}$ determines a family of circles with

$A$ spherical mothball has an initial radius of $3 \text{ cm}$. Due to evaporation, the radius of the ball reduces to $1 \text{ cm}$ in $4 \text{ months}$. In how many months would the mothball evaporate completely if the volume is lost at a rate proportional to the surface area?

Vedclass Test Series

Exam Paper Generator

Online Exam Module