Reena and Ruchira borrowed Rs 60-000 and Rs 50-000 respectively for a period of 3 years- Reena paid simple interset at the rate of 10-p-a while Ruhira paid compound interest at the rate of 10- p-a compounded annually- Who paid more interest and by how much-

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Standard VIII

Mathematics

Reena and Ruc...

Question

Reena and Ruchira borrowed $R s . 60, 000$ and $R s . 50, 000$ respectively for a period of $3$ years. Reena paid simple interset at the rate of $10 %$ per annum, while Ruchira paid compound interest at the rate of $10 %$ compounded annually. Who paid more interest and by how much?

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Solution

Case 1: [For Reena]
Principal amount $P = R s . 60, 000$
Time $(T) = 3$ years
Rate of interest $(R) = 10 %$ per annum
Simple interest $S . I = \frac{P R T}{100}$
$= \frac{R s . 60000 \times 10 \times 3}{100}$
$= R s . 18000$
Case 2: [For Ruchira]
Principal amount $= R s . 50, 000$
Time $(T) = 3$ years
Rate of interest $(R) = 10 %$ compounded annually.
So, $n = 3$
Now, The total amount on compounded annually is,
$A = P (1 + \frac{R}{100})^{n}$
$\Rightarrow A = R s . 50, 000 (1 + \frac{10}{100})^{3}$
$\Rightarrow A = R s . 50, 000 (1 + \frac{1}{10})^{3}$
$\Rightarrow A = R s . 50, 000 \times (\frac{11}{10})^{3}$
$\Rightarrow A = R s . 50, 000 \times \frac{11}{10} \times \frac{11}{10} \times \frac{11}{10}$
$\Rightarrow A = R s . 50 \times 1331$
$\Rightarrow A = R s . 66550$
Compound interest $(C . I) = A - P$
$\Rightarrow (C . I) = R s . 66550 - R s . 50, 000$
$\Rightarrow (C . I) = R s . 16, 550$
Therefore, Reena paid more.
More amount $= R s . 18000 - R s . 16, 550 = R s . 1450$

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Reena and Ruchira borrowed Rs. 60,000 and Rs. 50,000 respectively for a period of 3 years. Reena paid simple interset at the rate of 10% per annum, while Ruchira paid compound interest at the rate of 10% compounded annually. Who paid more interest and by how much?

Reena and Ruchira borrowed $R s . 60, 000$ and $R s . 50, 000$ respectively for a period of $3$ years. Reena paid simple interset at the rate of $10 %$ per annum, while Ruchira paid compound interest at the rate of $10 %$ compounded annually. Who paid more interest and by how much?