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Question
Find the difference between the compound interest and simple interest. On a sum of Rs 50,000 at 10% per annum for 2 years.
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Solution
Given:
P = Rs 50, 000
R = 10 % p. a.
n = 2 years
We know that amount A at the end of n years at the rate R % per annum when the interest is
compounded annually is given by A = P\[\left( 1 + \frac{R}{100} \right) . \]
\[ \therefore\text{ A = Rs }50, 000 \left( 1 + \frac{10}{100} \right)^2 \]
\[ =\text{ Rs }50, 000 \left( 1 . 1 \right)^2 \]
= Rs 60, 500
Also,
CI = A - P
= Rs 60, 500 - Rs 50, 000
= Rs 10, 500
We know that:
\[SI = \frac{PRT}{100}\]
\[ = \frac{50, 000 \times 10 \times 2}{100}\]
= Rs 10, 000
∴ Difference between CI and SI = Rs 10, 500 - Rs 10, 000
= Rs 500
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