## Simple Interest

**Points to Remember**

**1) Simple Interest:**If the interest on a sum borrowed is reckoned uniformly, for a certain period, then it is called as simple interest. It is a quick method of calculating interest charged on a loan. Simple interest can be easily determined by multiplying the interest rate by principal by the number of periods.

**2) Principal:**It is the money borrowed or lent out for a certain period of time.

**3) Interest:**Rate of money paid regularly for using money on lent.

**4) Total amount:**Sum of principal and simple interest.

**Important Formulae:**

**Simple interest on principal amount P for T years at the rate of R % is given as:**

1) Principal = | 100 × S.I. |

(R × T) |

2) Years = | (100 × S.I.) |

(P × R) |

3) Rate of Interest = | (100 × S.I.) |

(P × T) |

4) Simple Interest = | (P × R × T) |

100 |

**Quick tips and tricks**

1) The rate of interest is always calculated per year unless specifically noted.

2) If in any numerical, the time given is specified in months, then convert it into years by simply dividing number of months by 12. If time is given in days, then convert days into year by dividing it with 365.

a) S.I. = | (P × R × M) |

1200 |

b) S.I. = | (P × R × D) |

36500 |

3) Principal is the amount deposited or borrowed, so do not get confused between such terms.

4) Simple Interest = Principle x Rate of Interest X Time

a) S.I. = PRT ------------------- (If rate of interest is in decimal form)

b) S.I. = | (P × R × T) | ----------- (If rate of interest is in percent form) |

100 |

5) If sum of money becomes (z times) in (T) years at simple interest, then rate of interest (R) can be calculated using the formula:

Rate of Interest (R) % = | 100 (z – 1) |

T |

6) If sum of money becomes (z times) at rate of interest (R) % per annum at simple interest, then time (T) can be calculated using the formula:

Time (T) = | 100 (z – 1) |

R |

**Different types of questions asked in this chapter**

**Generally 3 basic types of questions discussed below are asked in the exams. Understanding and studying theses concepts will help in solving numerical related to this chapter.**

Type 1: Find simple interest

**Q 1.**What will be the simple interest on Rs. 80,000 at 16(2/3) % per annum for 9 months?

a. 8,000

b. 9,000

c. 10,000

d. 11,000

View solution

Correct Option: (c)**We are given: **

1) Principal = Rs. 80,000

2) Rate of interest = 16 | 2 | % |

3 |

Rate of interest = 16 | 2 | % = | 50 |

3 | 3 |

Time = | 9 | = | 3 | years |

12 | 4 |

Simple Interest = | (P × R × T) |

100 |

**Substituting the given values, we get**

Simple Interest = | 80,000 | × | 50 | × | 3 |

100 | 3 | 4 |

**Simple Interest = Rs.10,000**

**Q 2.**Find the simple interest on Rs. 5000 at 6 % per annum for the period from 5

^{th}Feb to 19

^{th}April, 2015.

a. Rs. 40

b. Rs. 50

c. Rs. 60

d. Rs. 70

View solution

Correct Option: (c)

We are given:

1) Principal = Rs. 5000

2) Rate of interest = 6 %

3) Time = 5^{th} Feb to 19^{th} April, 2015

First find the time period 5^{th} Feb to 19^{th} April, 2015

Feb = 28 – 5 = 23 days

March = 31 days

April = 19 days

Total days = 23 + 31 + 19 = 73 days**Convert days into years, by dividing it by 365**

Time = | 73 | = | 1 |

365 | 5 |

Simple Interest = | (P × R × T) |

100 |

= | [5000 × 6 × (1/5)] |

100 |

**Simple Interest = Rs. 60**

**Q 3.**Suresh borrows Rs. 10,000 for 2 years at 4 % p.a. simple interest. He lends it to Ramesh at 6 % p.a. for 2 years. Find his gain in this transaction per year.

a. Rs. 150

b. Rs. 200

c. Rs. 400

d. Rs. 450

View solution

Correct Option: (b)**We have to calculate the gain in 2 years. ****1) In case of Suresh**

S.I. | 10000 × 4 × 2 | = Rs. 800 |

100 |

**2) In case of Ramesh**

S.I. | 10000 × 6 × 2 | = Rs. 1200 |

100 |

Suresh has a pay a simple interest of Rs. 80 to the person from whom he borrowed Rs. 1000 and Ramesh has to pay Rs. 120 to Suresh.

Hence, gain in 2 years = 1200 – 800 = Rs. 400

But we are asked to find gain of Suresh per year. Therefore,

Gain in 1 year = 400 / 2 = Rs. 200