Compound Interest in Mathematics

 
 
Class—B.B.A-II semester
Subject—Mathematics
Topic—Compound Interest
Prepared By– Ms. Bhanu Sachdeva
                            (Assistant Professor)
 Department of Commerce and Management
  I.B.(PG) College,Panipat
      (Affiliated to Kurukshetra University,Kurukshetra)
 
COMPOUND INTEREST
 
KEYWORDS
:
Moneylender
Borrower
Principal
Rate
Interest
Amount
 
 
Explanation
 of keywords
 
Moneylender
: A moneylender is a person who lends
money which has to be paid back at a high rate of
interest.
Borrower
: A borrower is a person who gets money
from someone with intension of giving it back after a
period of time.
Principal
:The money borrowed by a borrower from a
moneylender is called a principal.
 
   EXPLANATION OF KEYWORDS
 
 Rate 
: The interest  paid for the use of Rs. 100 is called
rate percent.
 
Interest
: The extra amount paid by the borrower to
the lender is called interest.
 Amount
: The total money returned after a fixed time
is a amount.
            
Amount=Principal+Interest.
 
  
          
INTEREST
 
                  
Types of Interest
 
 Simple Interest
Compound Interest
 
SIMPLE INTEREST
 
 Simple interest: 
When interest is calculated on the
original principal for any length of time, it is called
simple interest.
 
 FORMULA OF SIMPLE INTEREST
 Simple interest = Principal×Time×Rate/100
i.e. S.I. = (P×R×T)/100
 
COMPOUND INTEREST
 
 Compound  interest: 
The difference between
original sum and final amount is called compound
interest.
 
FORMULA OF COMPOUND  INTEREST
                                C.I. = A-P
 
 
 
           
FORMULAS
 
 
FORMULAS  FOR  FINDING  AMOUNT
 Amount
(A) = P(1+r/100)
n
 Where n is number of time
period.
Applicable
 –when time is complete i.e 2years or 3years
Amount
 (A)=P(1+r/100)
i
 (1+fr/100)where i is an integer and
f is a fraction.
Applicable
-when time is not complete i.e 2.5years or
3.5years
Amount
 = P(1+r1/100)(1+r2/100)(1+r3/100)
Applicable
 -when rate of interest is  different for different
years
 
Example based on first formula
 
 Example1. Find the compound interest on Rs.8000 for 4
years at 10% per annum
.
Solution: Here principal(p)=Rs.8000,Rate(r)=10%per annum,
Time(t)=4 years
Using the formula,   A=P(1+r/100)
n
  we have
             A=8000(1+10/100)⁴
  
   =8000(110/100)⁴
             =Rs. 8000(11/10)⁴
             =Rs. 8000x11/10x11/10x11/10x11/10
             =Rs.11712.8
 therefore compound interest (C.I)=A-P=Rs.(11712.8-8000)
     
              =Rs.3712.80
 
 
 
EXAMPLE BASED ON SECOND FORMULA
 
Example : A man deposits Rs.3200 in a finance company for
2.5  years at 10% per annum.Find  the amount he received
Solution: Here P=Rs.3200,r=10% per annum
         t=2.5years
         A=P(1+r/100)
n
(1+fr/100)
            =3200(1+10/100)
2
(1+1/2*10/100)
            =3200(110/100)
2
(1+5/100)
            =3200(11/10)
2
(105/100)
            =3200*11/10*11/10*21/20
            =Rs.4065.6
 
Examle based on third formula
 
Example-A man deposited Rs.5000 in a bank for three
years. If he got compound interest at 4% for Ist year.3%
for second year and 2% for third year. Find the amount
he got at end of 3years.
  Solution:Here P = Rs.5000
     r1 =4%,r2=3%,r3=3%
Using    A=P(1+r1/100)(1+r2/100)(1+r3/100)
            A=5000(1+4/100)(1+3/100)(1+2/100)
            A=5000x104/100*103/100*102/100
            A=104*103*51/100=5463.12
 
 
       THANK YOU
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This detailed content explains the concept of compound interest in mathematics, covering key terms like moneylender, borrower, principal, rate, and amount. It also delves into simple interest, types of interest, and provides formulas for calculating compound interest based on different scenarios. Prepared by Ms. Bhanu Sachdeva, Assistant Professor at I.B. College, Panipat, this resource is beneficial for students studying finance and commerce.


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  1. ClassB.B.A-II semester Subject Mathematics Topic Compound Interest Prepared By Ms. Bhanu Sachdeva (Assistant Professor) Department of Commerce and Management I.B.(PG) College,Panipat (Affiliated to Kurukshetra University,Kurukshetra)

  2. COMPOUND INTEREST COMPOUND INTEREST KEYWORDS: Moneylender Borrower Principal Rate Interest Amount

  3. Explanation Explanation of keywords Moneylender: A moneylender is a person who lends money which has to be paid back at a high rate of interest. Borrower: A borrower is a person who gets money from someone with intension of giving it back after a period of time. Principal:The money borrowed by a borrower from a moneylender is called a principal.

  4. EXPLANATION OF KEYWORDS EXPLANATION OF KEYWORDS Rate : The interest paid for the use of Rs. 100 is called rate percent. Interest: The extra amount paid by the borrower to the lender is called interest. Amount: The total money returned after a fixed time is a amount. Amount= Amount=Principal+Interest Principal+Interest. .

  5. INTEREST Types of Interest Simple Interest Compound Interest

  6. SIMPLE INTEREST Simple interest: When interest is calculated on the original principal for any length of time, it is called simple interest. FORMULA OF SIMPLE INTEREST Simple interest = Principal Time Rate/100 i.e. S.I. = (P R T)/100

  7. COMPOUND INTEREST COMPOUND INTEREST Compound interest: The difference between original sum and final amount is called compound interest. FORMULA OF COMPOUND INTEREST C.I. = A-P

  8. FORMULAS FORMULAS FOR FINDING AMOUNT Amount(A) = P(1+r/100)nWhere n is number of time period. Applicable when time is complete i.e 2years or 3years Amount (A)=P(1+r/100)i(1+fr/100)where i is an integer and f is a fraction. Applicable-when time is not complete i.e 2.5years or 3.5years Amount = P(1+r1/100)(1+r2/100)(1+r3/100) Applicable -when rate of interest is different for different years

  9. Example based on first formula Example1. Find the compound interest on Rs.8000 for 4 years at 10% per annum. Solution: Here principal(p)=Rs.8000,Rate(r)=10%per annum, Time(t)=4 years Using the formula, A=P(1+r/100)nwe have A=8000(1+10/100) =8000(110/100) =Rs. 8000(11/10) =Rs. 8000x11/10x11/10x11/10x11/10 =Rs.11712.8 therefore compound interest (C.I)=A-P=Rs.(11712.8-8000) =Rs.3712.80

  10. EXAMPLE BASED ON SECOND FORMULA EXAMPLE BASED ON SECOND FORMULA Example : A man deposits Rs.3200 in a finance company for 2.5 years at 10% per annum.Find the amount he received Solution: Here P=Rs.3200,r=10% per annum t=2.5years A=P(1+r/100)n(1+fr/100) =3200(1+10/100)2(1+1/2*10/100) =3200(110/100)2(1+5/100) =3200(11/10)2(105/100) =3200*11/10*11/10*21/20 =Rs.4065.6

  11. Examle Examle based on third formula based on third formula Example-A man deposited Rs.5000 in a bank for three years. If he got compound interest at 4% for Istyear.3% for second year and 2% for third year. Find the amount he got at end of 3years. Solution:Here P = Rs.5000 r1 =4%,r2=3%,r3=3% Using A=P(1+r1/100)(1+r2/100)(1+r3/100) A=5000(1+4/100)(1+3/100)(1+2/100) A=5000x104/100*103/100*102/100 A=104*103*51/100=5463.12

  12. THANK YOU THANK YOU

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