Question

Find the sum of money on which the difference between compound interest and simple interest at the rate of 10% per annum for 2 years is 500.​

Answer 1

Given :

• ➻ Principal = Rs. 500
• ➻ Rate = 10 %
• ➻ Time = 2 years

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To Find :

• ➻ Find the sum of money at simple interest and compound interest.
• ➻ Find the difference.

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Solution :

~ Formula Used :

$\large{\blue{\bigstar}} \: \: {\underline{\boxed{\color{red}{\sf{ Simple \: Interest \: = \dfrac{Principal \times Rate \times Time}{100}}}}}}$

$\large{\blue{\bigstar}} \: \: {\underline{\boxed{\color{red}{\sf{ Compound \: Interest \: = Principal \bigg\lgroup 1 + \dfrac{Rate}{100} \bigg\rgroup ^{Time} - Principal }}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━}$

~ Calculating the Simple Interest :

${\longmapsto{\qquad{\sf{ S.I = \dfrac{ P \times R \times T }{100}}}}} \\ \\ \ {\longmapsto{\qquad{\sf{ S.I = \dfrac{500 \times 10 \times 2}{100}}}}} \\ \\ \ {\longmapsto{\qquad{\sf{ S.I = \dfrac{500 \times 20}{100}}}}} \\ \\ \ {\longmapsto{\qquad{\sf{ S.I = \cancel\dfrac{ 10000 }{ 100 }}}}} \\ \\ \ {\qquad{\textsf{ Simple \: Interest \: = {\green{\sf{ ₹ \: 100 }}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━}$

~ Calculating the Compound interest :

${\longmapsto{\qquad{\sf{ C.I = P \bigg\lgroup 1 + \dfrac{R}{100} \bigg\rgroup ^T - P }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ C.I = 500 \bigg\lgroup 1 + \dfrac{10}{100} \bigg\rgroup ^2 - 500 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ C.I = 500 \bigg\lgroup \cancel\dfrac{110}{100} \bigg\rgroup ^2 - 500 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ C.I = 500 \bigg\lgroup 1.10 \bigg\rgroup ^2 - 500 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ C.I = 500 \times 1.10 \times 1.10 - 500 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ C.I = 500 \times 1.21 - 500 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ C.I = 605 - 500 }}}} \\ \\ \ {\qquad{\textsf{ Compound Interest = {\pink{\sf{ ₹ \: 105 }}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━}$

~ Calculating the Difference :

${\longmapsto{\qquad{\sf{ Difference = C.I - S.I }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Difference = ₹ \: 105 - ₹ \: 100 }}}} \\ \\ \ {\qquad{\textsf{ Difference between the Interests = {\blue{\sf{ ₹ \: 5 }}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━}$

Therefore :

❝ Difference between both the interests is ₹ 5 .❞

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Answer 2

Question:-

Find the sum of money on which the difference between compound interest and simple interest at the rate of 10% per annum for 2 years is 500.

Given:-

• Principal (P) = ₹500.

• Rate (R) = 10%.

• Time (T) = 2 years.

To Find:-

• The sum of money on Simple Interest and Compound Interest.

• To Find Difference Between the Compound Interest and Simple Interest.

Solution:-

1st We Find Simple Interest:-

♤ Formula Used:-

$\large{\pink{\bigstar}} \: \: {\underline{\boxed{\color{blue}{\sf{ Simple \: Interest \: = \dfrac{Principal \times Rate \times Time}{100}}}}}}$

Calculating the Simple Interest.

$\sf \large \longmapsto \: S.I = \frac{500 \times 10 \times 2}{100}$

$\sf \large \longmapsto S.I = \frac{500 \times 100}{100}$

$\sf \large \longmapsto S.I = \frac{10,0{{ \cancel{00 }}}}{1{{ \cancel{00} }}}$

⟼ S.I = ₹100.

$\sf \large \longmapsto \red{ \boxed { \sf \: Simple \: Interest = ₹100.}}$

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2nd We Find Compound Interest:-

♤ Formula Used:-

$\sf \large{\pink{\bigstar}} \: \: {\underline{\boxed{\color{blue}{\sf{Compound \: Interest \: = Principal \bigg(1 + \frac{Rate}{100} \bigg) {}^{Time} \: - Principal}}}}}$

Calculating the Compound Interest.

$\sf \large \longmapsto C.I = P \bigg(1 + \frac{R}{100} \bigg) {}^{T} - P$

$\sf \large \longmapsto C.I = 500 \bigg(1 + \frac{10}{100} \bigg) {}^{2} - 500$

$\sf \large \longmapsto C.I = 500 \bigg( {{ \cancel{\frac{110}{100} }}}\bigg) {}^{2} - 500$

$\sf \large \longmapsto \: C.I = (1.1) {}^{2} - 500$

$\sf \large \longmapsto C.I = 500 \times 1.1 \times 1.1 - 500$

$\sf \large \longmapsto C.I = 500 \times 1.21 - 500$

$\sf \large \longmapsto C.I \: 605 - 500$

⟼ C.I = ₹105.

$\sf \large \longmapsto \green{ \boxed { \sf \: Compound \: Interest = ₹105.}}$

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Calculating the Difference.

● Difference = Compound Interest – Simple Interest

= 105 – 100

= ₹5.

Answer:-

$\sf \blue{ \therefore \: Difference \: Between \: compound \: } \\ \sf \blue{interest \: and \: simple interest \: = \red { ₹5.}}$

Hope you are have satisfied. ⚘