Question

The interest earned on ₹20,000 at the rate of 20% per annum for 1.5 years if compounded half-yearly is how much more than the simple interest earned on the same amount at the same rate of interest for the same period.​

Answer 1

Step-by-step explanation:

compounded half yearly which means

20000=principle, 20/2= rate of interest, time= 3 years

short cut method

20000

20000+2000---> 1st year

20000+2000+2000+200-----> 2nd year

20000+2000+2000+2000+200+200+200+20---->3rd year

Then the compound interest is 26620 at the end of 3rd year

simple interest is (P×R×T)/100= (20000×20×1.5)/100= 6000

difference between c.i and s.i is 20620

Answer 2

$\sf{\orange{\boxed{\huge{\mathsf{Compound \: Interest }}}}}$

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$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• Principle = Rs.20,000
• Rate = 20%
• Time = 1.5 years = 3 half years

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

• Compound Interest = ??

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

$\sf{\red{\boxed{\bold{Amount = P \bigg( 1 + \dfrac{r}{100}\bigg)^t}}}}$

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$\sf: \implies\: {\bold{ Amount = 20,000\bigg( 1 +\dfrac{20}{100}\bigg)^3}}$

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$\sf: \implies\: {\bold{ Amount = 20,000\bigg( 1 +\dfrac{2}{10}\bigg)^3}}$

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$\sf: \implies\: {\bold{ Amount = 20,000\bigg( \dfrac{10 + 2 }{10}\bigg)^3}}$

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$\sf: \implies\: {\bold{ Amount = 20,000\bigg(\dfrac{12}{10}\bigg)^3}}$

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$\sf: \implies\: {\bold{ Amount = 20,000\times\dfrac{12\times 12\times 12}{10\times 10 \times 10}}}$

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$\sf: \implies\: {\bold{ Amount = 20,00\times\dfrac{12\times 12\times 12}{10\times 10 }}}$

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$\sf: \implies\: {\bold{ Amount = 200\times\dfrac{12\times 12\times 12}{10}}}$

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$\sf: \implies\: {\bold{ Amount = 20\times12\times 12\times 12}}$

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$\sf: \implies\: {\bold{ Amount = 20\times 144\times 12}}$

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$\sf: \implies\: {\bold{ Amount = 20\times 1728}}$

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$\sf: \implies\: {\bold{ Amount = Rs. 34560}}$

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$\sf{\red{\boxed{\bold{CI = Amount - Interest}}}}$

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$\sf: \implies\: {\bold{ CI = Rs. 34560 - Rs.20000}}$

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$\sf: \implies\: {\bold{ CI = Rs. 14560}}$

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• Rs. 20000 will amount Rs.14560 as CI in 1.5 years at the rate 20% per annum compounded half yearly

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$\sf{\orange{\boxed{\huge{\mathsf{Simple \: Interest }}}}}$

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$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• Principle = Rs. 20000
• Rate = 20%
• Time = 1.5years = 3 half years

______________________

$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

• Simple Interest = ??

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

$\sf{\red{\boxed{\bold{SI = \dfrac{P\times R\times T}{100}}}}}$

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$\sf: \implies\: {\bold{ SI = \dfrac{20000\times 20\times 3}{100}}}$

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$\sf: \implies\: {\bold{ SI = \dfrac{2000\times 20\times 3}{10}}}$

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$\sf: \implies\: {\bold{ SI = 200\times 20\times 3}}$

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$\sf: \implies\: {\bold{ SI = 200\times 60 }}$

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$\sf: \implies\: {\bold{ SI = Rs. 12000}}$

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• Rs. 20000 will amount Rs. 12000 as simple interest in 1.5 years at 20% per annum

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$\sf{\orange{\boxed{\huge{\mathsf{Compare }}}}}$

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Rs. 14560 > Rs. 12000

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CI > SI

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Compare = Rs. 14560 - Rs. 12000

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Compare = Rs. 2560

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• CI is greater than SI by Rs. 2560

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