Find the amount and the compound interest on $R s 10, 000$ for $1 \frac{1}{2}$ years at $10 %$ per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?

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Solution

Compounded half yearly:
$A = P {(1 + \frac{r}{200})}^{2 n} \times (1 + \frac{b r}{100}) = 10000 {(1 + \frac{10}{200})}^{(2)} \times ⎛ ⎜ ⎜ ⎜ ⎝ 1 + \frac{\frac{1}{2} \times 10}{100} ⎞ ⎟ ⎟ ⎟ ⎠ = 10000 (1.1025) (1.05) = 11576.25$

Amount $= R s . 11, 576.25$
$C I = A - P = R s . 1576.25$

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Find the amount and the compound interest on Rs 10,000 for 112 years at 10% per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?

Compounded half yearly:A=P(1+r200)2n×(1+br100)=10000(1+10200)(2)×⎛⎜ ⎜ ⎜⎝1+12×10100⎞⎟ ⎟ ⎟⎠=10000(1.1025)(1.05)=11576.25Amount =Rs.11,576.25CI=A−P=Rs.1576.25

Find the amount and the compound interest on $R s 10, 000$ for $1 \frac{1}{2}$ years at $10 %$ per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?