Question

15. The compound interest on Rs.100 for 2years at the rate of 10% per annum compounded annually is


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Answer 1

Given :-

• Principal = ₹100
• Rate = 10% p.a
• Time = 2 years

To find :-

Compound interest

Formula to use :-

$Amount = Principal \bigg(1 + \dfrac{rate}{100} \bigg)^{time}$

Substituting the values,

$a = 100 \bigg(1 + \dfrac{10}{100} \bigg)^{2}$

$a = 100 \bigg( \dfrac{100 + 10}{100} \bigg)^{2}$

$a = 100 \bigg( \dfrac{110}{100} \bigg)^{2}$

$a = 100 \bigg( \dfrac{11 \cancel{0}}{10 \cancel{0}} \bigg)^{2}$

$a = 100 \bigg( \dfrac{11}{10} \bigg)^{2}$

$a = 100 \times \dfrac{11}{10} \times \dfrac{11}{10}$

By cancellation,

$amount = ₹121$

Compound interest = Amount - Principal

By substituting the values,

CI = ₹121 - ₹100

Compound interest = ₹21

Some more formulas :-

When interest is compounded half-yearly :-

$Amount = Principal \bigg(1 + \dfrac{rate}{200} \bigg)^{2 \times time}$

When interest is compounded quarterly :-

$Amount = Principal \bigg(1 + \dfrac{rate}{400} \bigg)^{4 \times time}$

Simple interest :-

$simple \: interest = \dfrac{principal \times time \times rate}{100}$