# Examples of Simple Interest

Example 1:
Find the simple interest on Rs. 3000 at a 7% rate of interest for one year.

Solution:
Let Principal = 3000, Rate of interest = 7%, $n = 1$

Simple interest $= \,\,\,\,\left( {{\text{Principal}}} \right)\left( {{\text{Rate}}} \right)\left( n \right) = \,\,\,\,\left( {3000} \right)\,\,7\% = \,\,\,\,3000 \times \,\frac{7}{{100}} = \,\,\,\,210$

Example 2:
Find the simple interest on Rs. 10,000 at the rate of 5% for 5 years. Also find the total amount after this time.

Solution:
Let Principal = 10,000 Rs., Rate = 5%, Time $= n = 5$

The amount of simple interest for 5 years is
$\begin{gathered} Interest\; = \,\,\,\,\left( {{\text{Principal}}} \right)\left( {{\text{Interest}}} \right)\left( {{\text{Time}}} \right) = \,\,\,\,\left( {10,000} \right)\left( {5\% } \right)\left( 5 \right) \\ Interest\;\; = \,\,\,\,\left( {10,000} \right)\left( {\frac{5}{{100}}} \right)\left( 5 \right)\,\,\,\,\, = 2,500 \\ \end{gathered}$

Hence the amount after 5 years ${\text{ = Principal}} + {\text{Interest}} = 10,000 + 2,500 = 12,500$

Example 3:
Find the simple interest on Rs. 156,00 for $1\frac{1}{2}$ years at the rate of 5% per annum. Also find the total amount.

Solution:
Let Principal = 15,600, Rate = 5% $= \frac{5}{{100}}$ $= 0.5$, Time = $1\frac{1}{2}$years $= \left( {1 + \frac{1}{2}} \right)\,\,{\text{years}}$ $= \frac{3}{2}\,{\text{years}}$

Simple interest for 5 years $= \,\,\,\,\left( {{\text{Principal}}} \right)\left( {{\text{Interest}}} \right)\left( {{\text{Time}}} \right) = \,\,\,\,\left( {15,600} \right)\left( {\frac{5}{{100}}} \right)\left( {\frac{3}{2}} \right) = \,\,\,\,1,170$

Amount ${\text{ = Principal}} + {\text{Interest}} = {\text{ }}15,600 + 1,170 = \,\,\,\,16,770$

Example 4:
Find the simple interest on Rs. 8,000 for 40 days, at 10% per annum.

Solution:
Let Principal = 8,000 Rs., Rate = 10% per annum, Time = 40 days $= \frac{{40\,{\text{years}}}}{{365}}$ $= \frac{8}{{73}}\,\,{\text{years}}$
Simple interest $= \,\,\,\,\left( {{\text{Principal}}} \right)\left( {{\text{Rate}}} \right)\left( n \right) = \,\,\,\,\left( {8,000} \right)\left( {\frac{{10}}{{100}}} \right)\left( {\frac{8}{{73}}} \right) = \frac{{6,400}}{{73}}$