Sudhir lent Rs 2000 at compound interest at 10 % payable yearly, While Prashant lent Rs 2000 at compound interest at 10 % payable half yearly. Find the difference in the interest received by Sudhir and Prashant at the end of one year?

byAmlesh Mahato •March 21, 2021

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Solution:

⇨In case of Sudhir

⇨Given

⇨p=2000

⇨r=10 %

⇨n=1 p.a.

⇨Then the annual Compound interest paid by Sudhir will be

$\large C.I=p\left \{ \left ( 1+\frac{r}{100} \right )^{n}-1 \right \}$

$\large \Rightarrow C.I=2000\left \{ \left ( 1+\frac{10}{100} \right )^{1}-1 \right \}$

$\large \Rightarrow C.I=2000\left \{ \frac{100+10}{100}-1 \right \}$

$\large \Rightarrow C.I=2000\times \frac{110-100}{100}$

$\large \Rightarrow C.I=2000\times \frac{10}{100}$

$\large \Rightarrow C.I=\frac{200000}{100}$

$\large \Rightarrow C.I=200$ Rs

⇨In case of Prashant
⇨Given
⇨p=2000
⇨r=10 %
⇨n=1 Half-yearly.
⇨Then the half-yearly Compound interest paid by Prashant will be

$\large C.I=p\left \{ \left ( 1+\frac{r}{2\times 100} \right )^{2n}-1 \right \}$

$\large \Rightarrow C.I=2000\left \{ \left ( 1+\frac{10}{200} \right )^{2\times 1}-1 \right \}$

$\large \Rightarrow C.I=2000\left \{ \left ( \frac{200+10}{200} \right )^{2}-1 \right \}$

$\large \Rightarrow C.I=2000\left \{ \left ( \frac{210}{200} \right )^{2}-1 \right \}$

$\large \Rightarrow C.I=2000\left \{ \frac{44100}{40000}-1 \right \}$

$\large \Rightarrow C.I=2000\times \frac{44100-40000}{40000}$

$\large \Rightarrow C.I=2000\times \frac{4100}{40000}$

$\large \Rightarrow C.I=\frac{8200000}{40000}$

$\large \Rightarrow C.I=\frac{820}{4}$

$\large \Rightarrow C.I=205$ Rs

⇨Therefore The difference in the interest received by Sudhir and Prashant at the end of one year Will be

= 205 - 200

= 5 Rs

Tags: Math-Class-8

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