In a bank, principal increases at the rate fo r% per annum. Find the value of r if ` 100 double itself in 10 years.
(Given loge 2 = 0.6931)
Given:
Here, p is the principal, r is the rate of interest per annum and t is the time in years.
Solving the differential equation we get,
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⇒
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As it is given that the principal doubles itself in 10 years, so
Let the initial interest be p1 (for t = 0 ), after 10 years p1 becomes 2p1.
Thus, for ( t = 0) …(i)
…(ii)
Substituting (i) in (ii), we get,
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⇒
⇒
⇒
⇒
Rate of interest = 6.931