Question

The principal increases continuously in a newly opened bank at the rate of $10%$ per year. An amount of Rs. 2000 is deposited with this bank. How much will it become after 5 years? ($e^{0.5} = 1.648$)

• A. 3926
• B. 3296
• C. 3692
• D. 3269

Hint:

Continuous growth formula: $A = Pe^{rt}$.

Answer 1

The Correct Option is B

Step 1: Concept
Continuous compounding is modeled by the differential equation $\frac{dP}{dt} = rP$.

Step 2: Meaning
Solution is $P(t) = P_0 e^{rt}$, where $P_0$ is the initial amount and $r$ is the rate.

Step 3: Analysis
$P = 2000 \cdot e^{0.1 \times 5} = 2000 \cdot e^{0.5}$. $P = 2000 \times 1.648$.

Step 4: Conclusion
$P = 3296$. Final Answer: (B)