Question

the compound interest on Rs.2,000 for 2 years at 20% per annum when compounded half yearly ,is​

Answer 1

$\huge{ \underline{ \underline \bold{answer}}}→$

we have,

• Principal,P = Rs. 2,000

for half yearly,

• Rate , R = 20/2 = 10%
• Time, n = 2 × 2 = 4

we know that,

$\boxed{ \bold{ \pink{amount ={ P \bigg\{1 + \frac{ R}{100}\bigg\}^{n} }}}}$

then here,

$\: \: \: \: \: \: \: \bold{A =2000 \bigg \{1 + \frac{10}{100} \bigg \} ^{4} }\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \bold{A = 2000 \bigg \{ \frac{100 + 10}{100} \bigg \}^{4} }\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \bold{ A = 2000 \bigg \{ \frac{11 \cancel{0}}{10 \cancel{0}} } \bigg \}^{4} \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \bold{A = 2\cancel{0} \cancel{0} \cancel{0} \times \frac{11}{1 \cancel{0}} \times \frac{11}{1 \cancel{0}} \times \frac{11}{1\cancel{0}} \times \frac{11}{10} } \: \: \: \\ \\ \implies \bold{A = \frac{ 2\times 11 \times 11\times 11\times 11}{10}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \bold{A = \frac{29282}{10}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \\ \\\implies\boxed{\bold{A=2928.2} }\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \:$

and we know that,

Compound Interest = Amount - Principal

$\implies \bold{C.I = 2928.2 - 2000 } \\ \\ \implies \boxed{ \orange{ \bold{C.I = 928.2}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

so, Compound Interest is Rs. 928.2

Answer 2

$\huge{ \underline{ \underline \bold{answer}}}→$

we have,

Principal,P = Rs. 2,000

for half yearly,

Rate , R = 20/2 = 10%

Time, n = 2 × 2 = 4

we know that,

$\boxed{ \bold{ \pink{amount ={ P \bigg\{1 + \frac{ R}{100}\bigg\}^{n} }}}}$

then here,

$\: \: \: \: \: \: \: \bold{A =2000 \bigg \{1 + \frac{10}{100} \bigg \} ^{4} }\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \bold{A = 2000 \bigg \{ \frac{100 + 10}{100} \bigg \}^{4} }\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \bold{ A = 2000 \bigg \{ \frac{11 \cancel{0}}{10 \cancel{0}} } \bigg \}^{4} \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \bold{A = 2\cancel{0} \cancel{0} \cancel{0} \times \frac{11}{1 \cancel{0}} \times \frac{11}{1 \cancel{0}} \times \frac{11}{1\cancel{0}} \times \frac{11}{10} } \: \: \: \\ \\ \implies \bold{A = \frac{ 2\times 11 \times 11\times 11\times 11}{10}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \bold{A = \frac{29282}{10}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \\ \\\implies\boxed{\bold{A=2928.2} }\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \:$

and we know that,

Compound Interest = Amount - Principal

$\implies \bold{C.I = 2928.2 - 2000 } \\ \\ \implies \boxed{ \orange{ \bold{C.I = 928.2}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

so, Compound Interest is Rs. 928.2