Question

The simple interest on a sum of money for 5 years is 3/5 of the sum. Find the rate per cent per annum ?​

Answer 1

Answer:

The rate of interest per annum is 12%.

Step-by-step explanation:

Let the amount be P. The simple on this amount for N years at the rate of R% per year can be calculated as,

$I=\dfrac{PNR}{100}$

Given that the interest for 5 years is equal to three-fifth of the initial amount. That is,

$I=\dfrac{3}{5}P$

Equating these equations, we obtain

$\implies \dfrac{PNR}{100}=\dfrac{3}{5}P$

Substitute the value of N,

$\implies \dfrac{P\times 5\times R}{100}=\dfrac{3}{5}P\\\\\implies \dfrac{ 5PR}{100}=\dfrac{3}{5}P\\\\\implies \dfrac{ 5R}{100}=\dfrac{3}{5}\\\\\implies 5\times 5R=3\times 100\\\\\implies 25R=300\\\\\implies R=\dfrac{300}{25}= 12$

So the annual rate of interest is 12%.