Quantitative Notes on Simple Interest

Quantitative 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 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 is (I+8)
interest for 2 yrs is Rs. 8
interest for 1 yr = 4
rate of interest = (4/100) × 100 = 4%
Example3: If the amount is (10/9) times of 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 of Principal and 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 deposit Rs.140 to the bank every year up to 5 years . The bank gives him 5% rate of interest simple annually. And at the end of 5 years he get total amount of Rs.770
So, 140 is the instalment, time is 5 years rate of interest is 5% and the amount or debt is Rs.770
This Instalment is also known as the annual payment. Debt is total amount, so don’t confuse between these two terms.
Installment =   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 if you forget formula then how to approach this question.
Let installment is X. There are 4 installments 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 based on Simple Interest.
Example5: 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
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
Example6: A sum of money doubles itself in 3 yrs at a 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
Example7: 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
Example8: Rs.4000 is divided into two parts such that if one part be invested at 3% and the other at 5%, the annual interest from both the investments is Rs. 144. Find each part.
Solution: Let the amount lent at 3% rate be Rs.X, then amount lent at 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: