A sum of money is put at compound interest for 2 years at $20 %$ p.a. It would fetch ₹ 482 more, if the interest were payable half-yearly, than if it were payable yearly. Find the sum.

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Solution

When the principal is compounded half-yearly
R = $\frac{R}{2}$ , n = $2 \times 2$
Amount = $P (1 + \frac{R}{100 \times 2})^{4}$
When the principal is compounded yearly
R = R, n = 2
Amount = $P (1 + \frac{R}{100})^{2}$
Hence,
$P [{(1 + \frac{R}{100 \times 2})}^{2 \times 2} - {(1 + \frac{R}{100})}^{2}] = 482$
$\Rightarrow P [{(1 + \frac{20}{100 \times 2})}^{4} - {(1 + \frac{20}{100})}^{2}] = 482$
$\Rightarrow P \times 0.0241 = 482 \Rightarrow p = ₹ 20000$

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A sum of money is put at compound interest for 2 years at 20% p.a. It would fetch ₹ 482 more, if the interest were payable half-yearly, than if it were payable yearly. Find the sum.

When the principal is compounded half-yearly R = R2 , n = 2×2 Amount = P(1+R100×2)4 When the principal is compounded yearly R = R, n = 2 Amount = P(1+R100)2 Hence, P[(1+R100×2)2×2−(1+R100)2]=482 ⇒P[(1+20100×2)4−(1+20100)2]=482 ⇒P×0.0241=482⇒p=₹20000

A sum of money is put at compound interest for 2 years at $20 %$ p.a. It would fetch ₹ 482 more, if the interest were payable half-yearly, than if it were payable yearly. Find the sum.