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 (e^0.5 = 1.648).

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Solution

$Let at any instant t, the principal be P . Here, it is given that the principal increases at the rate of 5 % per year . \frac{d P}{d t} = \frac{5 P}{100} \Rightarrow \frac{d P}{P} = \frac{1}{20} d t Integrating both sides, we get \ln P = \frac{t}{20} + \ln C . . . . (1) Initially at t = 0, it is given that P = R s 1000 . \ln 1000 = \ln C Substituting the value of \ln C in (1), we get \ln P = \frac{t}{20} + \ln 1000 Putting t = 10, we get \ln \frac{P}{1000} = 0.5 \Rightarrow \frac{P}{1000} = e^{0.5} \Rightarrow P = 1000 \times 1.648 = 1648 Therefore, Rs 1000 will be worth Rs 1648 after 10 years .$

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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).

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 (e^0.5 = 1.648).