For Rs 10,000 at 10% p.a. What would be the compound interest  (compounded half -yearly) after 2 years?

 

Given,

  Principal = Rs 10,000

Here rate is compounded half-yearly,

  So, rate of interest = R = 10/2 %

= 5%

      Time = 2 years

           n = number of half years

          n = 2 × 2

         n = 4

 

Amount = P (1+R/100)^n

      = 10,000 (1+5/100)^4

      = 10,000 (1+1/20)^4

      = 10,000 ((20 + 1)/20)^4

      = 10,000 (21/20)^4

      = 10,000 × 194481/160000

      = 194481/16

      = Rs 12155.06

 

Now,

Amount = Principal + Interest

12155.06 = 10,000 + Interest

Interest = 12155.06 − 10,000

Interest = Rs 2155.06

 

Suppose I have Rs 1000 and I put it in a bank on compound interest, where interest is compounded half-yearly. What would be the amount I have after 1 1/2 years, if interest rate is 20% pa.?

 

Given,

  P = Rs 1000

Here rate is compounded half-yearly,

  So, rate of interest = R = 20/2 %

 = 10%

 

       Time = 1 1/2 years

                            n = number of half years

     n = 2 × 1 1/2

 

     n = 2 × 3/2

                            n = 3

  Amount = P (1+R/100)^n

        = 1000 (1+10/100)^3

= 1000 (1+1/10)^3

= 1000 ((10 + 1)/10)^3

= 1000 (11/10)^3 

= 1000 × 1331/1000

= 1331

 

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

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.