# More Examples of Simple Interest

**To find the principal w**__hen interest, time, and rate are given:__

__Example 01__**:**

What amount was borrowed, for which the amount of interest is Rs.200 at the rate of 5% for 4 years?

__Solution__**:**

Let P = Principal , Rate = 5%, Interest = 200, time = *n* = 4, I = Interest

We know that

\[I = {\text{P}}\left( {\text{r}} \right)\left( n \right)\]

\[{\text{P}} = \frac{1}{{{\text{r}}n}}\,\,\,\, = \frac{{200 \times 100}}{{5 \times 4}}\,\,\,\, = 1000\]

**To find the principal w**__hen amount, rate, and time are given:__

__Example 02__**:**

If the amount if interest for 2 years at 6% is Rs.4,000, what was the principal?

__Solution__**:**

Let P = Principal, Rate = 6%, *n* = 2, A = 4,000

We know that

\[\begin{gathered} {\text{A}} = {\text{P}} + \Pr n \\ {\text{A}} = {\text{P}}\left( {1 + rn} \right) \\ \Rightarrow {\text{P}} = \frac{{\text{A}}}{{1 + {\text{r}}n}}\,\,\,\,\, = \frac{{4,000}}{{1 + \left( {6\% } \right)\left( 2 \right)}} \\ \Rightarrow P = \frac{{4,000}}{{1 + \left( {\frac{6}{{100}}} \right) \times 2}}\,\,\,\,\, = \frac{{4,000}}{{1 + \left( {.06} \right) \times 2}}\,\,\,\,\, = \frac{{4,000}}{{1.12}}\,\,\,\,\, = 3500 \\ \end{gathered} \]

**To find the rate w**__hen interest, time, and principal are given:__

__Example 03__**:**

The amount of simple interest for Rs.15,000 for 2 years is 1000, find the rate of interest.

__Solution__**:**

Let Principal = 15,000, Simple interest = I = 1000, Time = 2 years

Interest = P r *n*

\[ \Rightarrow {\text{r}} = \frac{1}{{{\text{P}}n}}\,\,\,\,\, = \frac{{1,000}}{{15,000 \times 2}} = \frac{{500}}{{150 \times 100}}\,\,\,\,\, = \frac{{3.33}}{{100}}\,\,\,\,\, = 3.33\% \]