Find the amount of money for which the difference between compound interest and simple interest over a 2-year period at 5% per annum equals ₹63.

Question

Accepted Answer

To solve this problem, we need to use the formula for the difference between compound interest and simple interest for a 2-year period.

**Step 1: Identify the key information.**
- Time period = 2 years
- Rate of interest = 5% per annum
- Difference between CI and SI = ₹63

**Step 2: Apply the formula for difference between CI and SI for 2 years.**
For a 2-year period, the difference between compound interest and simple interest can be calculated using:
$$
	ext{Difference} = P 	imes \left(\frac{r}{100}ight)^2
$$

Where:
- P = Principal amount (what we need to find)
- r = Rate of interest (5%)

**Step 3: Substitute the values into the formula.**
$$
63 = P 	imes \left(\frac{5}{100}ight)^2
$$
$$
63 = P 	imes \frac{25}{10000}
$$
$$
63 = P 	imes 0.0025
$$

**Step 4: Solve for the principal amount.**
$$
P = \frac{63}{0.0025} = 25200
$$

Therefore, the principal amount on which the difference between compound interest and simple interest for 2 years at 5% per annum equals ₹63 is ₹25,200.

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