Question

the difference between simple intrest and compound intrest on a sum for 3 years when the rate of intrest is 15% p.a is rs 720 what is priciple amount​

Answer 1

$\sf\large\underline\green{Let:}$

$\sf{\implies The\:sum\:be\:P}$

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

$\sf{\implies The\:sum=?}$

$\sf\large\underline\green{Solution:}$

• To calculate the sum , at first we have to calculate simple interest and compound interest separately then calculate the sum with the help calculating sum:]

$\sf\small\underline\red{Calculation\:for\:(SI):}$

$\sf\small\underline{Here,\:\:P=P\:\:,T=years\:\:,R=15\%:}$

$\tt{\implies SI=\dfrac{P*T*R}{100}}$

$\tt{\implies SI=\dfrac{P*3*15}{100}}$

$\tt{\implies SI=\dfrac{9P}{20}}$

$\sf\small\underline\red{Calculation\:for\:(CI):}$

$\sf\small\underline{Here,\:\:P=P\:\:,T=years\:\:,R=15\%:}$

$\tt{\implies CI=P\bigg(1+\dfrac{r}{100}\bigg)^n-P}$

$\tt{\implies CI=P\bigg(1+\dfrac{15}{100}\bigg)^3-P}$

$\tt{\implies CI=P\bigg(\dfrac{100+15}{100}\bigg)^3-P}$

$\tt{\implies CI=P\bigg(\dfrac{115}{100}\bigg)^3-P}$

$\tt{\implies CI=P\bigg(\dfrac{23}{20}\bigg)^3-P}$

$\tt{\implies CI=\dfrac{12167P}{8000}-P}$

$\tt{\implies CI=\dfrac{12167P-8000P}{8000}}$

$\tt{\implies CI=\dfrac{4167P}{8000}}$

• Calculate Principal with help of given difference (SI-CI) here the given difference is Rs.720:]

$\sf\blue{\implies Difference\:_{(CI-SI)}=720}$

$\tt{\implies CI=\dfrac{4167P}{8000}-\dfrac{9P}{20}=720}$

$\tt{\implies CI=\dfrac{4167P-3600P}{8000}=720}$

$\tt{\implies CI=\dfrac{567P}{8000}=720}$

$\tt{\implies CI=63P=640000}$

$\tt{\implies CI=P=10158.7302}$

$\sf\large{Hence,}$

$\sf\green{\implies The\:sum=Rs.10158.7302}$

Answer 2

$\bf\red{Answer - }$

$\sf\pink{Given - }$

T = 3 years.

R = 15%

CI - SI = Rs. 720

where

$\longrightarrow$T is time period.

$\longrightarrow$R is rate of interest.

$\longrightarrow$CI is compound interest.

$\longrightarrow$SI is simple interest.

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$\sf\pink{To \: find - }$

Principle/Sum $\longrightarrow$ S

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$\sf\pink{Formula \: used - }$

$\boxed{\bf SI = \dfrac{PRT}{100}}$

$\boxed{\bf CI = P(1 + \dfrac{R}{100} ) ^{n}-P}$

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$\bf\pink{Solution -}$

Calculating Simple interest -

$\longrightarrow$T = 3 years.

$\longrightarrow$R = 15%

$\sf SI = \dfrac{PRT}{100}$

$\implies$$\sf SI = \dfrac{P \times 3 \times 15}{100}$

$\implies$$\sf\pink{ SI = \dfrac{9P}{20}}$

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Calculating Compound interest -

$\longrightarrow$T = 3 years.

$\longrightarrow$R = 15%

$\sf CI = P(1 + \dfrac{R}{100} ) ^{n} - P$

$\implies$$\sf CI = P(1 + \dfrac{R}{100} ) ^{n} - P$

$\implies$$\sf CI = P(1 + \dfrac{15}{100} ) ^{3} - P$

$\implies$$\sf CI = P(\dfrac{115}{100} )^3 - P$

$\implies$$\sf CI = P (\dfrac{23^3}{20^3}) - P$

$\implies$$\sf CI = P(\dfrac{11267}{8000}) - P$

$\implies$$\sf CI = P(\dfrac{11267 - 8000}{8000})$

$\implies$$\sf\pink{ CI = P(\dfrac{4167}{8000})}$

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The difference of Compound and simple interest is equal to Rs. 720.

$\implies$$\tt 720 = \dfrac{4167P}{8000} - \dfrac{9P}{20}$

$\implies$$\tt 720 = \dfrac{4167P}{8000} - \dfrac{3600P}{8000}$

$\implies$$\tt 720 = \dfrac{4167P - 3600P}{8000}$

$\implies$$\tt 720 = \dfrac{567P}{8000}$

$\implies$$\tt 720 \times 8000 = 567P$

$\implies$$\tt P = Rs. 10158.73$

$\bf\red{Principle\: amount = Rs. 10158.73}$

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