Question

In a bank, the principal increases continuously at a rate of $x%$ per year. Then the rate $x$, if Rs.\ 100 doubles itself in 10 years, is ($\log 2 = 0.6931$)

• A. $6.93%$
• B. $9.63%$
• C. $6.09%$
• D. $3.69%$

Hint:

For continuous growth, use \(A = Pe^{rt}\).

Answer 1

The Correct Option is A

Concept:
Continuous growth: \[ P(t) = P_0 e^{rt} \] Step 1: Given condition. Initial amount = 100, final amount = 200, time = 10 years \[ 200 = 100 e^{rt} \]
Step 2: Simplify. \[ 2 = e^{10r} \]
Step 3: Take log. \[ \ln 2 = 10r \] \[ r = \frac{0.6931}{10} = 0.06931 \]
Step 4: Convert to percentage. \[ x = 0.06931 \times 100 = 6.93% \]
Step 5: Conclusion. \[ x = 6.93% \]