Let's do this by taking an example

 

For Rs 10,000 at 10% p.a. What would be the compound interest for 2 1/2 years?

 

Given,

  Principal = Rs 10,000

     R = 10% p.a

       Time = 2 1/2 years

 

Since time is in fraction,

  we use the formula

 

Compound interest for 2 1/2 years

    = Compound interest for 2 years  

   + SI for next 1/2 years

 

Compound interest for 2 years

Amount = P (1 + R/100) t

     = 10,000 (1 + 10/100) 2

     = 10,000 (1 + 1/10) 2

     = 10,000 ((10 + 1)/10) 2

     = 10,000 (11/10) 2

    = 10,000 × (121/100)

   = 100 × 121

  = Rs 12,100

 

Now,

  Amount = Principal + Interest

   12,100 = 10,000 + Interest

   12,100 − 10,000 = Interest

    2100 = Interest

    Interest = Rs 2100

 

Simple interest for 1/2 years

 

Principal will be the amount after 2 years

P = Rs 12100

R = 5% p.a

T = 1/2 years

 

SI = PRT/100

    = (12100 × 5 × 1/2)/100

    = (12100 × 5)/(100 × 2)

    = (121 × 5)/2

    = 605/2

    = Rs 302.5

Simple interest for 1/2 years = Rs 302.5

 

Now,

Compound interest for 2 1/2 years

= Compound interest for 2 years  + SI for next 1/2 years

   = 2,100 + 302.5

  = Rs 2402.5

 

∴ Compound interest after 2 1/2 years = Rs 2402.5

 

 

Suppose I have Rs 1000 and I put it in a bank on compound interest. What would be the amount I have after 1 3/4 years, it interest rate is 5% pa.?

 

Given,

Principal = Rs 1000

Rate = 5% p.a

Time = 1 3/4 years

 

Since time is in fraction

  We use the formula

 

Compound interest for 1 3/4 years

    = Compound interest for 1 years  + SI for next 3/4 years

 

Compound interest for 1 years

Amount = P (1 + R/100) T

      = 1000 (1 + 5/100) 1

      = 1000 (1 + 1/20)

      = 1000 ((20 + 1)/20)

      = 1000 (21/20)

      = 100 × 21/2

      = 50 × 21

      = Rs 1050

 

Now,

Amount = Principal + Interest

1050 = 1000 + Interest

1050 − 1000 = Interest

50 = Interest

Interest = Rs 50

 

Simple interest for 3 / 4 years

 

Principal will be the amount after 1 year

  P = Rs 1050

  R = 5% p.a

  T = 3/4 years

 

S.I = PRT/100

= (1050 × 5 × 3/4)/100

= (1050 × 5 × 3)/(100 × 4)

= (105 × 5 × 3)/(10 × 4)

= (21 × 5 × 3)/(2 × 4)

= 315/8

= Rs 39.375

 

3.jpg

Now,

Interest after 1 3/4 years = Compound interest for 1 year + Simple interest for next 3/4 year

       = 50 + 39.375

        = Rs 89.375

  1. Chapter 8 Class 8 Comparing Quantities
  2. Concept wise

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.