Q. Tom lent a sum of money at 20% compound interest for two years. If the interest is compounded half-yearly as opposed to annually he would earn Rs 964 more. The amount lent is

20000

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30000

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40000

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45000

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None of these

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Solution

The correct option is C 40000
For the given principal amount x

CI compounded half yearly $x \times {(1 + \frac{10}{100})}^{4} - x = \frac{4641 x}{10000}$

CI compounded annually $x \times {(1 + \frac{20}{100})}^{2} - x = .44 x = \frac{11 x}{25}$

$\frac{4641 x}{10000} - \frac{11 x}{25} = 964$

4641x - 4400x = 9640000

$x = \frac{9640000}{241}$

x = 40000

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Q. Tom lent a sum of money at 20% compound interest for two years. If the interest is compounded half-yearly as opposed to annually he would earn Rs 964 more. The amount lent is

The correct option is C 40000For the given principal amount x CI compounded half yearly x×(1+10100)4−x=4641x10000 CI compounded annually x×(1+20100)2−x=.44x=11x25 4641x10000−11x25=964 4641x - 4400x = 9640000 x=9640000241 x = 40000