Quantitative Aptitude Notes Part 5(SIMPLE INTEREST AND COMPOUND INTEREST)

SIMPLE INTEREST AND COMPOUND INTEREST

What is Interest?
When borrowed some money from other for the personal or commercial purpose we pay some additional money to him after a certain period of time is called Interest.

 

What is Simple Interest?

Simple interest is calculated only on the principal amount, or on that portion of the principal amount that remains.

 

What is Compound Interest?

Compound interest is interest added to the principal of a deposit or loan so that the added interest also earns interest from then on. This addition of interest to the principal is called compounding.

 

What is Principle?
The money borrowed for a certain time period called Principle or Sum.


What is Amount?
The Addition of Simple Interest and Principle is called the Amount.
A = S.I + P (Principle).
S.I = A (Amount) – P (Principle).


What is per annum means?
Per annul means for a year.

P = Principle, R = Rate of per annum, T = Number of years

 

 

 

Formulas Need to Remember
S.I =

P =

 

R =

Example:
Find the simple interest on Rs 400 for 4 years at 4 per cent ?

Answer:
SI = 400 x 4 x 4 / 100
Simple interest in 4 years is Rs 64 .

Example: Find the Simple Interest on Rs. 40000 at 25 / 4 % per annul for the period from 4th January, 2013 to 18th march, 2013.

Answer:
Step 1: First we calculate the period of time taken that is = January = (31 – 4) = 27 days, February = 28 days, March = 18 day. Add all together (27 + 28 + 18 ) = 73 / 365 year = 1 / 5 years.
Step 2: we know Principle P = 40000, and R = 25 / 4 % p.a.
Step 3: S.I = Rs. ( 40000 X 25 X 1 X 1 / 4 X 100 X 5 ) = Rs. 500
So the S.I is 500.

Example:
What is the rate of p.c.p.a ? If the simple interest accrued on amount of Rs.25500 at the end of 3 years is 9180.

 
Answer:
we know the formula is S.I = PRT / 100
So, S.I = 9180 , P = 25500 , T = 3 years , R = ?
9180 = 25500 x R x 3 / 100
R = 9180 / 765 = 12 %
so, rate of p.c.p.a = 12 %

Example: 
Sarikatakes a sum from Dinesh at simple interest at 25x / 2 per annul and amounts to Rs.3202.50after 6 years. Find the Sum or Principle taken by Sarika from Dinesh.
Answer:
First We consider sum is x and Rate percent is 25x / 2 and Time is 6 years, So
Step 1:Then  S.I. = Rs. P X R X T / 100 = 3x / 4.
Step 2: Amount = Sum + Simple Interest = x + 3x / 4 = 7x / 4.
Step 3: 7x / 4 = 3202.50 and x = 3202.50 X 4 / 7 = 1830.
Sarika taken sum from Dinesh is 1830.

Some important formulae of Compound Interest

 

Type I: When interest compounded yearly : A = P ( 1 + r / 100 )n

 

Type II: When interest compounded half – yearly :
Amount = P [ 1 + r / 2 / 100 ]4n or = P = [ 1 + r / 200 ] 2n

 

 

Type III: When interest compounded quarterly :
Amount = P [ 1 + r / 4 / 100 ]   or  = P [ 1 + r / 400 ] 4n

 

 

Example:
Principle is 15000 at rate percent 4% p.c.p.a for 2 years, and compound annually
Find the C.I.
Answer:
We apply the formula to obtain C.I that is C.I = p [(1 + r / 100)n – 1]
P = 15000.
R = 4%.
Time = 2 years.
= 15000 x [( 1 + 4 / 100)2 – 1].
= 15000 x [26×26/25×25 – 1]. [ as we put down (26 / 25)2]
= 15000 x 51 / 625 .
= 1224


Example:
The Simple Interest accrued on an amount of Rs.22,500 at the end of 3 years is Rs. 10800what would be the Compound Interest accrued on the same amount at the same rate at the end of two years ?

Answer:
Here is given amount = 22,500 , Time = Years 3 and S.I = 10800 so we need to find Rate percent.
Step 1: we know S.I = P x R x T / 100
10,800 = 22,500 x R x 3 / 100
R = 1080000 / 67500 = 16 % So R = 16 %.
Step 2: Compound Interest accrued on the same amount at the same rate at the end of two years
is we apply the formula
C.I = 22500 x (116 / 100 x 116 / 100 – 1 )
= 22500 x( 116 x 116/ 10000 – 1) = 22500 x( 13456 / 1000) – 1 = 22500 x (1.3456 – 1) = 22500 x 0.3456 =7776
So the C.I end of two years is 7776.

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