8.  Find the amount and the compound interest on Rs 10,000 for  1\frac{1}{2}   years at 10% per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?
 

Answers (1)

Principal = Rs.10,000

Time =   1\frac{1}{2}   years

Rate = 10% per annum

CASE 1  Interest on compounded half yearly.

Rate = 10% per annum  = 5 % per half yearly

  T= 1\frac{1}{2} years,n=3

A= P\left ( 1+\frac{R}{100} \right )^{n}

A= 10000\left ( 1+\frac{5}{100} \right )^{3}

A= 10000\left ( 1+0.05 \right )^{3}

A= 10000\left ( 1.05 \right )^{3}

A= 11576.25 = Amount

CI = Amount - principal

CI  = 11576.25-10000

CI = 1576.25

CASE 2     Interest on compounded anually

Rate = 10% per annum

T= 1\frac{1}{2} years ,n=1

A= P\left ( 1+\frac{R}{100} \right )^{n}

A= 10000\left ( 1+\frac{10}{100} \right )^{1}

A= 10000\left ( 1+0.1\right )^{1}

A= 10000\left ( 1.1\right )^{1}

A= 11000 = Amount

CI = Amount - principal

CI  = 11000-10000

CI = 1000

 

Interest for half years on 11000 = 

\frac{P\times R\times T}{100}

=\frac{11000\times 10\times \frac{1}{2}}{100}

= 55\times 10

= 550

Total interest = 1000+550

                    = RS 1550

Since 1576.25 > 1000

Thus, interest would be more in CASE 1 i.e. compounded half yearly

 

 

 

 

 

          

 

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