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Calculate compound interest on $₹ 1000$ over a period of 1 year at 10%

per annum if interest is compounded half yearly.

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102.50

104.50

105.50

108.50

answer is A.

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Detailed Solution

Given
P = 1000
R = 10 %
Interest rate for six months: 1/2 x 10% = 5%
T = 1 years
Due to the fact that interest is compounded every six months, there are two conversion periods every year.
So,

n = 2

A = P {(1 + \frac{R}{100})}^{n}

A = 1000 {(1 + \frac{5}{100})}^{2}

A = 1000 {(1 + \frac{1}{20})}^{2}

A = 1000 {(\frac{21}{20})}^{2}

A = 1000 (\frac{21}{20})

(\frac{21}{20})

A = 1000

\frac{21}{20}

\frac{21}{20}

A = (\frac{5 X 21 X 21}{2})

A

(\frac{2205}{2})

= Rs . 1102.50

Compound interest = A−P =1102.50 – 1000 = Rs.102.50
So the Compound interest is 102.50
The Correct Answer is 1.

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