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 log_e 2 = 0.6931)

Question

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 log e 2 = 0.6931)

Philoid · Accepted Answer

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,

⇒

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,

⇒

Rate of interest = 6.931

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)