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# Find the amount and the compound interest on Rs 10,000 for 1.5 years at 10% per annum compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?

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?

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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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