In a bank, principal increases continuously …

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In a bank, principal increases continuously at the rate of 5% per year. In how many years ₹1000 double itself?

Posted by Tanushri Bhayani 2 years, 1 month ago

CBSE > Class 12 > Applied Maths

2 answers

Preeti Dabral 2 years, 1 month ago

Let P be the principal at any time t. According to the given problem, $\frac{d p}{d t}=\left(\frac{5}{100}\right) \times \mathrm{P}$
or $\frac{d p}{d t}=\frac{\mathrm{P}}{20}$ ...(i)
separating the variables in equation (i), we get
$\frac{d p}{\mathrm{P}}=\frac{d t}{20}$ ...(ii)
Integrating both sides of equation (ii), we get
log P = $\frac{t}{20}$ + C₁
or P = $e^{\frac{t}{20}} \cdot e^{\mathrm{C}_{1}}$
or P = $\mathrm{C} e^{\frac{t}{20}}$ (where e^C₁= C) ...(iii)
Now, P = 1000, when t = 0
Substituting the values of P and t in (iii), we get C = 1000. Therefore, equation (iii), gives
P = 1000 e^t/20
Let t years be the time required to double the principal. Then 2000 = 1000 e^t/20 $\Rightarrow$ t = 20 log_e2.

1Thank You

Tanushri Bhayani 2 years, 1 month ago

Thames bro 😘

0Thank You

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