Question

(e) ₹ 10000 for 1 year at 8% per annum compounded half yearly.

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Answer 1

principle = 10000

rate of interest = 8% p.a compounded half yearly

time = 1 years

now , there are two half years in a year . therefore compounding has to be 2 times

and rate = half of 10% = 5% half yearly .

therefore required amount = 10000 ( 1 + 4/100) ^ 2

= Rs.10816

and compound interest , C.I. = amount - principle = ( rs10816 - 10000) = rs.816

Answer 2

Given,

• Principal (P) = 8,000
• Rate (R) = 8% Per annum compounded half Yearly
• = $\sf \frac{8}{2}$% Per half year
• = 4% Per Half year

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Time (N) = 1 Year

= 2 half years.

$\sf \:Amount (A) = P (1+ \frac{r}{100} ) ^{h}$

$\longrightarrow \sf 10000 (1+ \frac{4}{100} )²$

$\longrightarrow \sf 10000 ( \frac{ 100+4}{100})^{2}$

$\longrightarrow \sf 100000 \times ( \frac{104}{100} ) ^{2}$

$\longrightarrow \sf 10000 \times (\frac{ 104 \times 104 }{100 \times 100})$

$\longrightarrow \sf 10000 \times \frac{ 10816}{ 10000}$

$\longrightarrow \sf \: 10816$

$\sf$

$\underline{ \red{ \sf \: Amount = Rs \: 10816}}$

Now,

Amount = Principal + Interest

$\leadsto \sf \: 10816 = 10000 + Interest$

$\sf \leadsto Interest = 10816 - 10000$

$\sf \leadsto \: Interest = 816$

Thus,

$\underline{ \purple{ \sf \: Amount = Rs \: 10,816}}$

$\underline{ \purple{ \sf \: Compound \: Interest = Rs \: 816}}$