Question

At what rate percent per annum will a sum of 4000 yield a compound interest of rupees 410 in 2 years

Answer 1

Principal = P = Rs. 4000
Let rate of interest be x%
Time = n = 2 years
Therefore, Compound Interest =
$p( {1 + r \div 100)}^{n} - p \\ = 4000( {1 + x \div 100)}^{2} - 4000 \\ = 4000 (( {1 + x \div 100)}^{2} - 1) \\ = 4000(( {100 + x \div 100) }^{2} - 1)$
ATP,
$4000(( {100 + x \div 100)}^{2} - 1) = 410 \\ = > ( {100 + x \div 100)}^{2} - 1 = 410 \div 4000 \\ = > ( {100 + x \div 100)}^{2} - 1 = 41 \div 400 \\ = > ( {100 + x \div 100)}^{2} = 41 \div 400 + 1 \\ = > ( {100 + x \div 100)}^{2} = 41 + 400 \div 400 \\ = > ( {100 +x \div 100)}^{2} = 441 \div 400 \\ = > ( 100 + x \div 100) = \sqrt{441 \div 400} \\ = > 100 + x \div 100 = 21 \div 20 \\ 2000 + 20x = 2100 \\ 20x = 2100 - 2000 \\ 20x = 100 \\ x = 100 \div 20 \\ x = 5$
Therefore, Rate of interest = 5%



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