Question

What will be the difference between simple and compound interests at the rate of 10%p.a. on a sum of Rs 1000 after 2 years? (give full explanation)

Answer 1

Answer:

Answer: Principal sum = ₹1000, interest rate = 10%p.a. , time= 4yrs. Simple interest= P.R.T/100 = 1000×10×4/100 = 400. Compound interest= P{1+ R/100}™ - P =1000{1+10/1000}^4-1000 = 1464.1 - 1000 = 464.1 Thus difference in interests= 464.1 - 400 = ₹64.1

Answer 2

Given :

• Principal = Rs.1000
• Rate = 10 %
• Time = 2 years

To Find :

• Simple Interest = ?
• Compound Interest = ?
• Difference = ?

Solution :

✭ Formula Used :

• ${\underline{\boxed{\purple{\sf{ S.I = \dfrac{P \times R \times T}{100} }}}}}$

• ${\underline{\boxed{\purple{\sf{ C.I = P \bigg\lgroup 1 + \dfrac{R}{100} \bigg\rgroup^n - P }}}}}$

Where :

• ➬ S.I = Simple Interest
• ➬ C.I = Compound Interest
• ➬ R = Rate
• ➬ T = Time
• ➬ n = Time

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✭ Calculating the Simple Interest :

${:\implies{\qquad{\sf{ S.I = \dfrac{P \times R \times T}{100} }}}} \\ \\ \\ \ {:\implies{\qquad{\sf{ S.I = \dfrac{1000 \times 10 \times 2}{100} }}}} \\ \\ \\ \ {:\implies{\qquad{\sf{ S.I = \dfrac{1000 \times 20}{100} }}}} \\ \\ \\ \ {:\implies{\qquad{\sf{ S.I = \dfrac{20000}{100} }}}} \\ \\ \\ \ {:\implies{\qquad{\sf{ S.I = \cancel\dfrac{20000}{100} }}}} \\ \\ \\ \ {\qquad \; \; {\therefore \; {\underline{\boxed{\pink{\pmb{\frak{ Simple \; Interest = ₹ \; 200 }}}}}}}}$

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✭ Calculating the Compound Interest :

${\dashrightarrow{\qquad{\sf{ C.I = P \bigg\lgroup 1 + \dfrac{R}{100} \bigg\rgroup^n - P }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ C.I = 1000 \bigg\lgroup 1 + \dfrac{10}{100} \bigg\rgroup^2 - 1000 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ C.I = 1000 \bigg\lgroup 1 + \cancel\dfrac{10}{100} \bigg\rgroup^2 - 1000 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ C.I = 1000 \bigg\lgroup 1 + 0.10 \bigg\rgroup^2 - 1000 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ C.I = 1000 \bigg\lgroup 1.10 \bigg\rgroup^2 - 1000 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ C.I = 1000 \times 1.10 \times 1.10 - 1000 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ C.I = 1000 \times 1.21 - 1000 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ C.I = 1000 \times 1.21 - 1000 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ C.I = 1210 - 1000 }}}} \\ \\ \\ \ {\qquad \; \; {\therefore \; {\underline{\boxed{\orange{\pmb{\frak{ Compound \; Interest = ₹ \; 210 }}}}}}}}$

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✭ Calculating the Difference :

${\longmapsto{\qquad{\sf{ Difference = Compound \; Interest - Simple \; Interst }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ Difference = 210 - 200 }}}} \\ \\ \\ \ {\qquad \; \; {\therefore \; {\underline{\boxed{\red{\pmb{\frak{ Difference = ₹ \; 10 }}}}}}}}$

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✭ Therefore :

❛❛ Difference between the interests is ₹ 10 . ❜❜

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