The simple interest on a sum of money is \(\frac{4}{5}\) of the principal. Find the rate of simple interest if both the rate of interest and time are numerically equal.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(4\sqrt{5}\)% P.A.
Simple interest is \(\displaystyle SI=\frac{P\times R\times T}{100}\). Here \(SI=\frac{4}{5}P\) and the rate and time are equal, so \(T=R\).
Putting \(SI=\frac{4}{5}P\) and \(T=R\) in the formula: \(\displaystyle \frac{4}{5}P=\frac{P\times R\times R}{100}\)
\(P\) cancels from both sides: \(\displaystyle R^2=\frac{4}{5}\times100=80\)
\(R=\sqrt{80}=\sqrt{16\times5}=4\sqrt{5}\)
The rate is \(4\sqrt{5}\)% per annum (about 8.94%), for a time of \(4\sqrt{5}\) years.