Question

Reena and Ruchira borrowed rupees 60000and50000 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%p.a. compounded anually. Who paid more interest and by how much ?

Answer 1

Principal amount for Reena P = $60000

Rate of interest  R =10%

Time T = 3 years

Simple interest I = P×R×T

I = 60000×0.10×3 = $ 18000

Principal for Ruchira P = $50000

Rate of interest I = 10%

Time T = 3 years

Compound interest = P[1+R]ⁿ

= $50000.[1+0.10]^{3}$

=$50000.(1.1)^{3}$

= $66550

Hence Ruchira pays more interest than Reena by $66550-$18000 = $48550

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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