Question

the difference between the annual and semi annual compound interest on the sum of money is rs482 at the rate of 20 per annum for 2yeara. find the sum
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Answer 1

Qᴜᴇsᴛɪᴏɴ :-

The difference between the annual and semi annual compound interest on the sum of money is Rs.482 at the rate of 20 per annum for 2years . find the sum ?

Sᴏʟᴜᴛɪᴏɴ :-

→ successive Rate of 20% for 2 Years = 2*20 + (20*20/100) = 40 + 4 = 44%.

And, when interest is compounded semi - Annually,

→ Rate = (20/2) = 10% .

→ Time = 2 * 2 = 4 Years.

So,

→ successive Rate of 10% for 4 Years = (2*10 + (10*10/100) = 21% Now, => 21*2 + (21*21/100) = 42 + 4.41 = 46.41% .

A/q,

→ (46.41%) - 44% = 482

→ 1% = (482/2.41)

→ 100% = (482/2.41) * 100 = Rs.20000 (Ans.)

Hence, The Required sum is Rs.20000 .

Answer 2

Answer:

✩ Let the Principal for Interest be P.

⠀

$\bigstar\:\sf when ;\:compounded \:annually\\\\\bullet\:\sf Rate\:(R)=20\%\\\\\bullet\:\sf Time\:(T)=2\:years \\\\ \\\bigstar\:\sf when ;\:compounded \:semi-annually\\\\\bullet\:\sf Rate\:(r)=\dfrac{20\%}{2} =10\%\\\\\bullet\:\sf Time\:(t)=2\:years \times 2 = 4\:years$

$\rule{100}{0.8}$

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$:\implies\sf Semi\: Annual-Annual=Rs.\:482\\\\\\:\implies\sf \bigg(P \times \dfrac{100 + r}{100}\bigg)^t-\bigg(P \times \dfrac{100 + R}{100}\bigg)^T=482\\\\\\:\implies\sf P\left[\bigg(\dfrac{100 + r}{100}\bigg)^t - \bigg(\dfrac{100 + R}{100}\bigg)^T\right] = 482\\\\\\:\implies\sf P\left[\bigg(\dfrac{110}{100}\bigg)^4 - \bigg(\dfrac{120}{100}\bigg)^2\right] = 482\\\\\\:\implies\sf P\left[\bigg(\dfrac{11}{10}\bigg)^4 - \bigg(\dfrac{12}{10}\bigg)^2\right] = 482\\\\\\:\implies\sf P\left[\bigg(\dfrac{14641}{10000}- \dfrac{144}{100}\bigg)\right] = 482\\\\\\:\implies\sf P\bigg(\dfrac{14641 - 14400}{10000}\bigg) = 482\\\\\\:\implies\sf P \times \dfrac{241}{10000} = 482\\\\\\:\implies\sf P = 482 \times \dfrac{10000}{241}\\\\\\:\implies\sf P = 2 \times 10000\\\\\\:\implies\underline{\boxed{\textsf{P = Rs.\:20,000}}}$

⠀

$\therefore\:\underline{\textsf{Hence, required sum will be \textbf{Rs. 20,000}}}.$