If the simple interest on a sum at 4% per annum for 2 years is Rs 80, then the compound interest on the same sum for the same period is-

byAmlesh Mahato •March 10, 2021

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Solution:

⇨Given

⇨r = 4%

⇨ n= 2

⇨S.I.= 80

⇨Using Simple Interest formula

$If the simple interest on a sum at 4% per annum for 2 years is Rs 80, then the compound interest on the same sum for the same period is-$

$\large \Rightarrow 80=\frac{p\times 4\times 2}{100}$

$\large \Rightarrow 8000=8p$

$\large \Rightarrow p=\frac{8000}{8}$

$\large \Rightarrow p=1000$ Rs

⇨Then Compound interest will be

$\large C.I=A-P$

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

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

$\large \Rightarrow C.I=1000\left \{ \left ( 1+\frac{4}{100} \right )^{2}-1 \right \}$

$\large \Rightarrow C.I=1000\left \{ \left ( 1+\frac{4}{100} \right )^{2}-1 \right \}$

$\large \Rightarrow C.I=1000\left \{ \left ( \frac{104}{100} \right )^{2}-1 \right \}$

$\large \Rightarrow C.I=1000\left \{ \frac{10816}{10000}-1 \right \}$

$\large \Rightarrow C.I=1000\left \{ \frac{10816-10000}{10000} \right \}$

$\large \Rightarrow C.I=1000\times \frac{816}{10000}$

$\large \Rightarrow C.I= \frac{816000}{10000}$

$\large \Rightarrow C.I=81.6$ Rs

Tags: Math-Class-8