Question

Reena and Ruchira borrowed 60,000 and 50,000 respectively for a period of 3 years. Reena paid simple interest at the rate of 10% p.a., while Ruchira paid compound interest at the rate of 10% pa.compounded annually. Who paid more interest and by how much? ​

Answer 1

Solution

It is given that Reena borrowed ₹60,000 and Ruchira borrowed ₹50,000 for a time 3years. Also given that Reena paid Simple Interest whereas Ruchira paid Compound Interest with the rate of interests 10% per annum for both. We have to find who paid more interest and by how much. So, Let's find:-

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Calculating Reena's Simple Interest (SI)

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Principal(P) = ₹60,000

Time(T) = 3years

Rate(R) = 10% p.a.

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${\bf{S.I.= \dfrac{P \times R \times T}{100} }}$

$\sf{ = \dfrac{600 \: \cancel{00}\times 10 \times 3}{1 \cancel{00}}}$

$\sf{ = 600 \times 10 \times 3}$

$\sf={₹18,000.}$

Simple Interest = ₹18,000.

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Calculating Ruchira's Compound Interest (CI)

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Principal(P) = ₹50,000

Time(n) = 3years

Rate(R) = ₹10% p.a.

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$\bf{A=P\bigg(1+\dfrac{R}{100}\bigg)^n}$

$\sf{ = 50000 \bigg(1+ \cancel\dfrac{10}{100} \bigg)^{3}}$

$\sf{ = 50000 \bigg(1 + \dfrac{1}{10} \bigg)^{3} }$

$\sf{ = 50000 \bigg( \dfrac{10 + 1}{10} \bigg)^{3} }$

$\sf{ = 50000 \bigg( \dfrac{11}{10} \bigg)^{3} }$

$\sf{ = 50 \: \cancel{000}\times \dfrac{1331}{1 \cancel{000}} }$

$\sf{ = 50 \times 1331}$

$\sf{A=66550}$

C.I. = A - P

C.I. = 66550 - 50000

Compound Interest = ₹16,550.

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Difference of interests = S.I. - C.I.

Difference of interests = ₹18,000 - ₹16,550

Difference of interests = ₹1,450.

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$\therefore \sf{\underline{Reena \: paid \: more \: interest \: by \: ₹1,450.}}$

Hence, solved!! ✓.

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Additional Information

Some Important formulas of SI

• A = P + SI
• P = A - SI
• I = A - P
• A = P(1+ R×T/100)
• P = 100×SI/R×T
• R = 100×SI/P×T
• T = 100×SI/P×R.

Some important formulas of CI

When Compounded Half yearly.

$\sf{A = P\bigg(1 +\dfrac{R}{200}\bigg)^{2n}}$

When compounded Quarterly

$\sf{A = P\bigg(1+\dfrac{R}{400}\bigg)^{4n}}$

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Answer 2

$\large\underline{\underline{\red{\pmb{\sf{ \:Given :-}}}}}$

• Reena and Ruchira borrowed 60000 and 50000 for a period of three years. Reena payed back this amount at the 10 % simple interest while Ruchira payed back this amount at 10 % compounded annually.

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$\large\underline{\underline{\blue{\pmb{\sf{ \:To \: Find :-}}}}}$

• Who paid more interest and by how much ?

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$\large\underline{\underline{\orange{\pmb{\sf{ \:Solution :-}}}}}$

~ Formula Used :

$\large{\gray{\bigstar}} \: \: \: {\underline{\boxed{\red{\sf{ S.I = \dfrac{P \times R \times T}{100}}}}}}$

$\large{\gray{\bigstar}} \: \: \: {\underline{\boxed{\red{\sf{ C.I = P \bigg\lgroup 1 + \dfrac{R}{100} \bigg\rgroup^T - P }}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━━}$

~ Calculating the Interest paid by Reena :

Here :

• ➳ P = 60000
• ➳ R = 10 %
• ➳ T = 3 years

Calculating Starts :

${\twoheadrightarrow{\qquad{\sf{ Interest{\small_{(Reena)}} = \dfrac{P \times R \times T}{108}}}}} \\ \\ \ {\twoheadrightarrow{\qquad{\sf{ Interest{\small_{(Reena) }} = \dfrac{ 60000 \times 10 \times 3}{100}}}}} \\ \\ \ {\twoheadrightarrow{\qquad{\sf{ Interest{\small_{(Reena) }} = \dfrac{1800000}{100}}}}} \\ \\ \ {\twoheadrightarrow{\qquad{\sf{ Interest{\small_{(Reena) }} = \cancel\dfrac{1800000}{100}}}}} \\ \\ \ {\qquad{\sf{ Interest \: paid \: by \: Reena \: = {\color{orange}{\sf{ ₹ \: 18000}}}}}}$

~ Calculating the Interest paid by Ruchira :

Here :

• ➳ P = 50000
• ➳ R = 10 %
• ➳ T = 3 years

Calculating Starts :

${\twoheadrightarrow{\qquad{\sf{ Interest{\small_{(Ruchira)}} = P \bigg\lgroup 1 + \dfrac{R}{100}\bigg\rgroup^T - P }}}} \\ \\ \ {\twoheadrightarrow{\qquad{\sf{ Interest{\small_{(Ruchira)}} = 50000 \bigg\lgroup 1 + \dfrac{10}{100}\bigg\rgroup^3 - 50000 }}}} \\ \\ \ {\twoheadrightarrow{\qquad{\sf{ Interest{\small_{(Ruchira)}} = 50000 \bigg\lgroup \dfrac{110}{100}\bigg\rgroup^3 - 50000 }}}} \\ \\ \ {\twoheadrightarrow{\qquad{\sf{ Interest{\small_{(Ruchira)}} = 50000 \bigg\lgroup \cancel\dfrac{110}{100} \bigg\rgroup^3 - 50000 }}}} \\ \\ \ {\twoheadrightarrow{\qquad{\sf{ Interest{\small_{(Ruchira)}} = 50000 \bigg\lgroup 1.10 \bigg\rgroup^3 - 50000 }}}} \\ \\ \ {\twoheadrightarrow{\qquad{\sf{ Interest{\small_{(Ruchira)}} = 50000 \times 1.331 - 50000 }}}} \\ \\ \ {\twoheadrightarrow{\qquad{\sf{ Interest{\small_{(Ruchira)}} = 66550 - 50000 }}}} \\ \\ \ {\qquad{\sf{ Interest \: paid \: by \: Ruchira \: = {\color{darkblue}{\sf{ ₹ \: 16550}}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━━}$

~ Calculating the Difference :

${:\implies{\qquad{\sf{ Difference = Interest{\small_{(Reena) }} - Interest{\small_{(Ruchira)}} }}}} \\ \\ \ {:\implies{\qquad{\sf{ Difference = S.I - C.I}}}} \\ \\ \ {:\implies{\qquad{\sf{ Difference = ₹ \: 18000 - ₹ \: 16550 }}}} \\ \\ \ {\qquad{\sf{ Difference \: in \: both \: Interest \: = {\color{maroon}{\sf{ ₹ \: 1450}}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━━}$

Therefore :

❝ Reena paid more interest and by ₹ 1450 . ❞

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