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

rate of interest = 10% per annum

time = 1 1/2 years = 3 half yearly.

if compounded half yearly, amount = $10000*(1+\frac{10}{2*100}{)}^{3}$

$=10000*(1+\frac{1}{20}{)}^{3}\phantom{\rule{0ex}{0ex}}=10000*\frac{{21}^{3}}{{20}^{3}}\phantom{\rule{0ex}{0ex}}=10000*\frac{9261}{8000}\phantom{\rule{0ex}{0ex}}=11576.25/-$

thus interest = 11576.25 - 10000 = 1576.25/-

case II; if amount is compounded yearly.

amount at the end of 1st year = $10000*(1+\frac{10}{100}{)}^{1}=10000*\frac{11}{10}=11000/-$

interest for the half year = $\frac{11000*10*1}{100*2}=550/-$

thus the total interest when compounded annually

= (11000-10000)+550

=1000+550

=1550/-

thus the interest is more when compounded half yearly.

hope this helps you

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