Question

Simple interest on a certain sum of money for 3 years at 5% per annum is ₹5250. What will be
the compound interest on that sum at the same rate for the same period?​

Answer 1

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Answer 2

Given:

• Simple interest on a certain sum of money for 3 years at 5% per annum is ₹5250. What will be the compound interest on that sum at the same rate for the same period?

Answer:

• ₹ 5515.88.

Formulae used:

• $\bf{S.I = \dfrac{P ×R×T}{100} }$
• $\bf{A = P \bigg( 1 + \dfrac{R }{100} \bigg) }^{T}$

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Solution:

• S.I = ₹ 5250

• R = 5%

• Time = 3 years

$\\ \therefore \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{S.I = \dfrac{P ×R×T}{100} } \\ \\ \sf \: \: \: \implies \: \: \: \: \: \: \sf{5250 = \dfrac{P ×5×3}{100} } \\ \\ \: \: \: \: \: \: \: \: \: \implies \sf \: \: \: \: \: \: \: \: \: \: \: P \: = ₹ \: \dfrac{5250 \times 100}{5 \times 3} \\ \\ \: \: \: \: \: \: \: \: \: \implies \sf \: \: \: \: \: \: \: \: \: \: \: P \: = ₹ \: \dfrac{5250 \times \cancel{100}}{ \cancel{5 }\times 3} \\ \\ \: \: \: \: \: \: \: \implies \sf \: \: \: \: \: \: \: \: \: \: \: \: P \: = ₹ \: \dfrac{5250 \times 20}{ 3} \\ \\ \sf \implies \: \: \: \: \: \: \: \: \: \: \: P \: = ₹35000 \: \: \: \: \:$

When interested is compounded annually,

$\sf{A = P \bigg( 1 + \dfrac{R }{100} \bigg) }^{T} \\ \\ \: \: \: \: \sf \: \: \: \: \: \: \: \: \: \: \: { = ₹ \: 35000 \bigg( 1 + \dfrac{5}{100} \bigg) }^{3} \\ \\ \: \: \: \: \sf \: \: \: \: \: \: \: \: \: \: \: { = ₹ \: 35000 \bigg( 1 + \dfrac{1}{20} \bigg) }^{3} \: \: \: \\ \\ \: \: \: \: \: \: \: \: \: \: \: { = ₹ \sf 35000 \bigg( \dfrac{21}{20} \bigg) }^{3} \: \: \: \: \: \: \: \: \ \: \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf= ₹ \: 35000 \: \times \: \frac{21}{20} \times \frac{21}{20} \times \frac{21}{20} \\ \\ \sf \: = ₹ \: \frac{324135}{8} \: \: \: \: \: \: \: \: \: \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sf \: ₹ \: 40516.875 \: ≈ ₹ \: 40516.88$

Compound interest = Amount – Principal

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= ₹(40516.88–35000)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= ₹ 5516.88

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⠀⠀⠀⠀⠀⠀⠀⠀Hope it helps!!

⠀⠀⠀⠀⠀⠀Stay home! Stay safe!