To calculate Simple interest, we use the formula,

Simple Interest = $\frac{P \times R \times T}{100}$

where, P is the principal (in dollar), R is the rate per annum and T is the time (in years)

Now, in order to calculate time when interest and principal is given we get,

I = $\frac{P \times R \times T}{100}$

Multiply by 100 on both sides,

$100 \times I$ = $100 \times $$\frac{ P \times R \times T}{100}$

$100 \times I$ = $P \times R \times T$

Divide by P on both sides,

$\frac{100 \times I}{P}$ = $\frac{P \times R \times T}{P}$

$\frac{100 \times I}{P}$ = $R \times T$

Divide by R on both sides,

$\frac{100 \times I}{P \times R}$ = $T$

$T$ = $\frac{100 \times I}{P \times R}$

Here, we take time (T) in years. If you want to find the interest in months, then you can't directly substitute the months in T but have to convert the months into years.

The following table shows how the time given in months can be converted in terms of years:

**Months ** |
** Years ** |

1 |
$\frac{1}{12}$ |

2 |
$\frac{2}{12}$ = $\frac{1}{6}$ |

3 |
$\frac{3}{12}$ = $\frac{1}{4}$ |

4 |
$\frac{4}{12}$ = $\frac{1}{3}$ |

5 |
$\frac{5}{12}$ |

6 |
$\frac{6}{12}$ = $\frac{1}{2}$ |

7 |
$\frac{7}{12}$ |

8 |
$\frac{8}{12}$ = $\frac{2}{3}$ |

9 |
$\frac{9}{12}$ = $\frac{3}{4}$ |

10 |
$\frac{10}{12}$ = $\frac{5}{6}$ |

11 |
$\frac{11}{12}$ |

12 |
$\frac{12}{12}$ = 1 |

**Example 1:**

How much time will the simple interest on a certain sum be 0.125 times the principal at 10% per annum.

**Solution:**

Suppose Principal, P = 1 dollar

Interest, I = 0.125 dollars

Rate, R = 10% per annum

I = $\frac{P \times R \times T}{100}$

Time, T = $\frac{100 \times I}{P \times R}$

= $\frac{100 \times 0.125}{1 \times 10}$

= 1.25 years

**Example 2:**

What sum of money lent out at 6.25% per annum simple interest produces 37.50 dollars as interest in 8 months?

**Solution:**

Interest, I = 37.50 dollars

Time, T = 8 months = $\frac{8}{12}$ years = $\frac{2}{3}$ years

Rate, R = 6.25% per annum

Since, I = $\frac{P \times R \times T}{100}$

So, P = $\frac{100 \times I}{R \times T}$

= $\frac{100 \times 31.50}{6.25 \times (2/3)}$

= 900 dollars

**Example 3:**

Find the interest on 1200 dollars at 6% per annum for 146 days.

**Solution:**

The interest is 6% per annum.

It means 6% for 365 days.

Therefore, rate of interest per day = $\frac{6}{365}$

Rate of interest for 146 days = $\frac{146 \times 6}{365}$

= $\frac{146 \times 6}{365 \times 100}$

Hence, Interest = $1200 \times $$\frac{146 \times 6}{365 \times 100}$

= 28.8 dollars