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Question

The compound interest on $$₹\ 6250$$ at $$ 8 \%$$ per annum for $$1$$ year, compounded half-yearly, is


A
₹ 500
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B
₹ 510
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C
₹ 550
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D
₹ 512.50
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Solution

The correct option is B ₹ 510

Given:

Present value $$= ₹\ 6250$$

Interest rate= $$8\ %$$ per annum

Time $$=1$$ year compounded half-yearly

To find the amount we have the formula,

Amount $$(A) = P (1+(r/100))^n$$

where $$P$$ is present value, $$r$$ is rate of interest, $$n$$ is time in years

Now substituting the values in above formula we get,

$$\therefore A = 6250 (1 +(8/2)/100)^2$$
$$\Rightarrow A = 6250 (1+4/100)^2$$
$$\Rightarrow A = 6250 (1+1/25)^2$$
$$\Rightarrow A = 6250 (26/25)^2$$
$$\Rightarrow A = 10 × 26 × 26$$
$$\Rightarrow A = ₹\ 6760$$

∴ Compound interest $$= A – P$$

$$= 6760 – 6250 = ₹\ 510$$

Mathematics

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