Overview: Simple & Compound Interest | Quantitative Techniques for CLAT PDF Download

Simple Interest

Consider you have deposited Rs 100 for 2 years on 10% Simple interest per annum, then we have

Simple interest for 1^st year

Thus after one year amount will become = 100 + 10 = Rs 110

Simple interest for 2^nd year

Here note that in 2^nd year interest is not calculated on amount (Rs 110) but Principal i.e, Rs 100.
Thus  Simple interest after two years =Rs 10 + Rs 10= Rs 20.
It can also be calculated be using formula –

Simple interest

• Here P = Principal / amount invested/amount borrowed.
• R = Rate of interest per annum.
• T =time in years.
• &  the final Amount = Principal + Simple interest

Thus for above example Simple interest

Also the final amount will be Rs 20 + Rs 100 = Rs 120.
Note : If rate of interest is not given in per annum then change the time according to the period over which interest is given.
For example : If interest is given as 10 % per quarter for 2years , then the time will have to be changed into quarters.
Time = 2 years = 2× 4 = 8 quarters
Thus Simple interest on Rs 100

Basics of Compound Interest

Again Consider you have deposited Rs. 100 for 2 years on 10% Compound interest per annum, then we have.

Compound interest after 1^st year
Thus after one year amount will become = 100+ 10 = Rs 110

Compound interest for 2^nd year

Here note that in 2^nd year interest is  calculated on amount ( Rs 110) and not on Principal i.e, Rs 100.

Thus  Compound interest after two years = Rs 10+ Rs 11= Rs 21

Final Amount = 100+ 21 =Rs 121

We can also find this using direct formula as given below-

For Amount we can use –
Note
When compound interest Compounded half yearly, then R% become and time T becomes 2T. For quarterly compounding we can change the rate and time accordingly

• Difference between SI and CI when Principal, Rate and time period is same
  • For two years,
  • For three years,
• For 1st year simple interest and Compound Interest will be same.
• If there are distinct ‘rates of interest’ for different years like R1 , R2 & R3 for 1st ,2nd and 3rd year respectively then we have

Let’s Take Some Previous Years Questions 

Q1: A sum of 1600 gives a simple interest of 252 in 2 years and 3 months. Calculate the rate of interest per annum.
Sol: We know


Q2: A sum of money deposited at simple interest amounts to 880 in 2 years and to 920 in 3 years. Find the sum.
Sol: Amount after two years = Rs 880
Amount after three years = Rs 920
Thus interest obtained per year = 920- 880 = Rs 40
For two years interest = 40×2 = Rs 80
Therefore Principal = 880-80 = Rs 800

Q3: Find the rate of simple interest for which a sum of money becomes 5 times of itself in 8 years.
Sol: Let the principal be P
Since Sum becomes 5 times of itself.

Q4: In how many years will 2,000 amounts to 2420 at 10% per annum if Compounded annually?
Sol: T= 2 years

Q5: A sum becomes 4500 after two years and 6750 after four years at compound interest.Find the sum.
Sol: Let the principal be x
We have
Dividing B by A , we get
Comparing Equation A with C, we get
Sum = Rs 3000