Quantity I: Ram invested a sum of Rs. 52,000 in a scheme offering compound interest at the rate of 10\% per annum. Find the interest earned by him after 3 years.

Quantity II: Rahim invested Rs. 28,750 in a scheme offering simple interest at the rate of 20\% per annum. Find the interest earned by him after 3 years.

Compare Quantity I and Quantity II.

Question

Quantity I: Ram invested a sum of Rs. 52,000 in a scheme offering compound interest at the rate of 10\% per annum. Find the interest earned by him after 3 years.

Quantity II: Rahim invested Rs. 28,750 in a scheme offering simple interest at the rate of 20\% per annum. Find the interest earned by him after 3 years.

Compare Quantity I and Quantity II.

Accepted Answer

**Solution:**

1. Calculate Compound Interest (CI) earned by Ram:

- Principal, $ P = 52000 $
- Rate, $ r = 10\% = 0.10 $
- Time, $ t = 3 $ years

Formula for amount with compound interest:

$$ A = P \times (1 + r)^t $$

Calculate amount:

$$ A = 52000 \times (1.1)^3 = 52000 \times 1.331 = 69212 $$

Compound Interest earned:

$$ CI = A - P = 69212 - 52000 = 17212 $$

2. Calculate Simple Interest (SI) earned by Rahim:

- Principal, $ P = 28750 $
- Rate, $ r = 20\% = 0.20 $
- Time, $ t = 3 $ years

Formula for simple interest:

$$ SI = \frac{P \times r \times t}{100} $$

Calculate interest:

$$ SI = \frac{28750 \times 20 \times 3}{100} = 28750 \times 0.6 = 17250 $$

3. Compare the two interests:

- Quantity I (CI) = Rs. 17212
- Quantity II (SI) = Rs. 17250

Since $ 17212 < 17250 $, Quantity I < Quantity II.

**Answer:** Quantity I < Quantity II

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