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प्रश्न
In a bank principal increases at the rate of 5% per year. An amount of Rs 1000 is deposited with this bank, how much will it worth after 10 years (e0.5 = 1.648).
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उत्तर
Let at any instant t, the principal be P .
Here, it is given that the principal increases at the rate of 5 % per year .
\[\frac{dP}{dt} = \frac{5P}{100}\]
\[ \Rightarrow \frac{dP}{P} = \frac{1}{20}dt\]
Integrating both sides, we get
\[\ln P = \frac{t}{20} + \ln C ...........(1) \]
Initially at t = 0, it is given that P = Rs 1000 .
\[\ln 1000 = \ln C\]
Substituting the value of ln C in (1), we get
\[\ln P = \frac{t}{20} + \ln 1000\]
\[\text{ Putting }t = 10, \text{ we get }\]
\[\ln \frac{P}{1000} = 0 . 5\]
\[ \Rightarrow \frac{P}{1000} = e^{0 . 5} \]
\[ \Rightarrow P = 1000 \times 1 . 648\]
\[ = 1648\]
Therefore, Rs 1000 will be worth Rs 1648 after 10 years .
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