Question

Find the compound interest on 7500 for one year at 8% per annum compounded half-yearly. Also, find the amount.

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Answer 1

Answer:

Find the amount of compound interest for Rs 7500 for 1 year at 8% per annum compounded half-yearly. = 8784. Therefore, the amount is Rs 8784.

Answer 2

S O L U T I O N :

$\underline{\bf{Given\::}}$

• Principal, (P) = Rs.7500
• Rate, (R) = 8% p.a
• Time, (n) = 1 year

$\underline{\bf{Explanation\::}}$

As we know that formula of the compounded half-yearly;

$\boxed{\bf{Amount = Principal\bigg(1+\frac{R/2}{100} \bigg)^{2n}}}$

A/q

$\mapsto\tt{Amount = P\bigg(1+\dfrac{R}{2\times 100} \bigg)^{2n}}$

$\mapsto\tt{Amount = 7500\bigg(1+\dfrac{8}{2\times 100} \bigg)^{2\times 1}}$

$\mapsto\tt{Amount = 7500\bigg(1+\dfrac{8}{200} \bigg)^{2}}$

$\mapsto\tt{Amount = 7500\bigg(1+\cancel{\dfrac{8}{200}} \bigg)^{2}}$

$\mapsto\tt{Amount = 7500\bigg(1+\dfrac{1}{25} \bigg)^{2}}$

$\mapsto\tt{Amount = 7500\bigg(\dfrac{25+1}{25} \bigg)^{2}}$

$\mapsto\tt{Amount = 7500\bigg(\dfrac{26}{25} \bigg)^{2}}$

$\mapsto\tt{Amount = \cancel{7500} \times \dfrac{26}{\cancel{25}} \times \dfrac{26}{\cancel{25} }}$

$\mapsto\tt{Amount =Rs.(12 \times 26 \times 26)}$

$\mapsto\bf{Amount =Rs.8112}$

Now, as we know that compound Interest;

→ C.I. = Amount - Principal

→ C.I. = Rs.8112 - Rs.7500

→ C.I. = Rs.612

Thus,

The compound Interest & amount will be Rs.612 & Rs.8112 .