CSIR-NET General Aptitude: Short Notes on Simple Interest!

Short Notes On Simple Interest

The CSIR NET 2022-23 Exam preparation required well-developed study notes for the candidates to prepare. Here are the Study Notes developed by the subject experts for the General Aptitude Short Notes on 'Simple Interest'.

Example 2: If the principal is 100 Rs. The difference of Simple Interest for 4yrs and 6yrs is Rs 8. Calculate the rate of simple interest.
Solution: In simple interest questions, interest always remains the same for a year if the principal rate of interest is constant for the same.
Let Interest for 4 yrs is I, then interest for 6 yrs be (I+8)
interest for 2 yrs is Rs. 8
interest for 1 yr = 4
rate of interest = (4/100) × 100 = 4%

Example 3: If the amount is (10/9) times the Principal and rate of interest and time, both are numerically equal. Then, what is the rate of interest per annum?
Solution: Let Principal is P. Given, numerically R = T
Interest = Amount – principal
I = (10/9)P – P
I = P/9 (Interest is in the multiples of Principal)
Now, I =[(P×R×T)/100]
P/9 = (P× R× T)/100
R² = 100/9 (using, R=T)
R = (10/3)%
We can also say the time period is (10/3)years.

Short approach: Whenever Interest is in multiple Principal and the Rate of Interest and Time period is equal.

Annual Instalments for Simple Interest:

Let's discuss a real example to understand  instalment concepts:
A person deposits Rs.140 to the bank every year for up to 5 years. The bank gives him a 5% rate of interest simply annually. And at the end of 5 years, he gets a total amount of Rs.770
So, 140 is the instalment, the time is 5 years rate of interest is 5%, and the amount of debt is Rs.770
This Instalment is also known as the annual payment. Debt is the total amount, so don’t confuse these two terms.

Instalment =   where A = debt, r = rate of interest and t = time period

Example4: What annual payment will discharge a debt of Rs.848 in 4yrs at 4% per annum simple interest?

In case you forget the formula, then how to approach this question?
Let instalment is X. There are 4 instalments, and rate of interest is also 4%
Debt (A) = four installments + (r%) × installments × (0+1+2+… (t-1))
So, 848 = 4X + (4%)(X)(0+1+2+3)
      848 = 4X+
      848 = 4X+
      848 = 424X/100
      X = 200

Some Important examples are based on Simple Interest.

Example 5: A sum amounts to Rs. 702 in 2 years and Rs. 783 in 3 years. Calculate the sum, rate of interest and the amount after 5 years.
Solution: Amount for 2 years(A₂) = 702
The amount for 3 years (A₃)= 783
Interest for 1 year (I) = 783-702 = 81
So Sum = A₂ – 2I = 702 – 2×81
              = 702-162 = 540
rate of interest = (81/540)×100
                             = 15%
Amount after 5 years = Sum+5I
                                    = 540+ 5×81
                                    = 945

Example 6: A sum of money doubles itself in 3 yrs at simple interest. In how many yrs will it amount to 8 times itself?
Solution: Doubles in 3 yrs
 3 times in 3× 2 = 6yrs
4 times in 3× 3 = 9yrs
8 times in 3× 7 = 21yrs

Example 7: Atul and Vijay are friends. Atul borrowed a sum of Rs.400 at 5% per annum simple interest from Vijay. He returns the amount with interest after 2 yrs. Vijay returns to Atul 2% of the total amount returned. How much did Atul receive?
Solution: After 2 yrs, amount returned to Vijay = 400+ (400*5*2)/100 = Rs 440
Amount returned to Atul = 2% of 440 = 8.8

Example 8: Rs.4000 is divided into two parts such that if one part is invested at 3% and the other at 5%, the annual interest from both investments is Rs. 144. Find each part.
Solution: Let the amount lent at a 3% rate be Rs. X, then the amount lent at a 5% rate is 4000-X
So, 3% of X + 5% of (4000-X) = 144
   5% of 4000 – 2% of X = 144
  200 – 2% of X = 144
  2% of X = 56
  X = (56/2)×100
 X = 2800
And 4000 -X = 1200.

How to solve this Question by Alligation Method:
First, we will calculate the net rate of interest for Rs. 144 on 4000
So, net rate = (144/4000)× 100 = 3.6%

Apply Allegation:

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