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Overview: Simple & Compound Interest | Quantitative Aptitude (Quant) - CAT 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 1st year

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

Simple interest for 2nd year

Overview: Simple & Compound Interest | Quantitative Aptitude (Quant) - CAT

Here note that in 2nd 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
Overview: Simple & Compound Interest | Quantitative Aptitude (Quant) - CAT

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


Compound interest

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

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

Compound interest for 2nd year

Here note that in 2nd 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-
Overview: Simple & Compound Interest | Quantitative Aptitude (Quant) - CAT

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
Overview: Simple & Compound Interest | Quantitative Aptitude (Quant) - CAT

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

The document Overview: Simple & Compound Interest | Quantitative Aptitude (Quant) - CAT is a part of the CAT Course Quantitative Aptitude (Quant).
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FAQs on Overview: Simple & Compound Interest - Quantitative Aptitude (Quant) - CAT

1. What is simple interest?
Ans. Simple interest refers to the interest earned or paid on the principal amount of a loan or investment. It is calculated by multiplying the principal by the interest rate and the time period.
2. How is simple interest different from compound interest?
Ans. Simple interest is calculated only on the principal amount, whereas compound interest is calculated on both the principal and the accumulated interest. Compound interest usually results in higher interest earnings compared to simple interest over a longer period of time.
3. How can I calculate the simple interest for a given loan or investment?
Ans. To calculate simple interest, you need to know the principal amount, the interest rate, and the time period. The formula for simple interest is: Interest = (Principal x Rate x Time) / 100. You can plug in the values and calculate the interest.
4. Is simple interest commonly used in financial institutions?
Ans. Yes, simple interest is commonly used in various financial transactions, especially for short-term loans and investments. It is easier to calculate and understand compared to compound interest, making it ideal for simple financial transactions.
5. Can you provide an example of simple interest calculation?
Ans. Certainly! Let's say you have invested $1,000 at an interest rate of 5% per year for a period of 3 years. To calculate the simple interest, you can use the formula: Interest = (Principal x Rate x Time) / 100. Plugging in the values, we get: Interest = (1000 x 5 x 3) / 100 = $150. Therefore, the simple interest earned on the investment would be $150.
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