Question

what is the difference between amounts for 2 years and 3 years for rs. 500 at 10% compound interest ?

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Answer 1

Answer:

Answer Expert Verified · rate = 10% · principal = ₹500 · time = 2 years.

Answer 2

Formula to be used ☞

$\purple\odot$ $\red {A = P (1 + \frac{R}{100})^{n}}$

$\purple\odot$ $\red {CI = P (1 + \frac{R}{100})^{n}-P}$

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Given,

$\sf \pink{Principle = ₹500}$

$\sf\pink{ Rate\: of\: interest = 10 \%}$

$\sf\pink{ Time_1 = 2 \: years}$

$\sf\pink{ Time_2 = 3 \: years}$

$\large\underline\purple {1st \: Amount = P (1 + \frac{R}{100})^{n}}$

➝

$\implies \tt₹500(1 + \frac{10}{100} ) ^{2} \\ \\ \implies \tt \: ₹500( \frac{100 + 10}{100} )^{2} \\ \\ \implies \tt \: ₹500( \frac{110}{100} ) ^{2} \\ \\ \implies \tt \: 5 \cancel{00} \times \frac{11 \cancel0}{1 \cancel0 \cancel0} \times \frac{11 \cancel0}{1 \cancel{00}} \\ \\ \implies \tt \: 5 \times 11 \times 11 \\ \\ \therefore \tt \: ₹605$

$\large\underline\purple {2nd \: Amount = P (1 + \frac{R}{100})^{n}}$

➝

$\implies \:₹500(1 + \frac{10}{100} )^{3} \\ \\ \implies \: ₹500( \frac{100 + 10}{100} ) ^{3} \\ \\ \implies \: ₹500( \frac{110}{100} ) ^{3} \\ \\ \implies \: ₹5 \cancel{00} \times \frac{11 \cancel0}{1 \cancel{00} } \times \frac{11 \cancel0}{10 \cancel0} \times \frac{11 \cancel0}{1 \cancel0 \cancel0} \\ \\ \implies \frac{\: 5 \times 11 \times 11 \times 11 }{10} \\ \\ \implies \: \frac{6655}{10} \\ \\ \therefore \: ₹665.5$

⟹ Difference = 2nd (A) - 1st (A)

⟹ ₹ 665.50 - ₹605

$\therefore$ ₹ 60.5[Ans]

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$\large \fbox \purple{Hope \: it \: helps \: you}$