2. On what sum of money will the difference between the compound interest and simple interest for 3 years be equal to \( ₹ 930 \), if the rate of interest charged for both is \( 10 \% \) p.a.?

To find the sum of money (principal) where the difference between compound interest and simple interest over 3 years is ₹ 930 at a rate of 10% per annum, we can use the formula: Difference = Compound Interest - Simple Interest = \( P \times \left( \left(1 + \frac{r}{100}\right)^n - 1 - \frac{rn}{100} \right) \). Here, \( r = 10 \), \( n = 3 \), and the difference is ₹ 930. Plugging in the values, we get: \[ 930 = P \left( \left(1 + \frac{10}{100}\right)^3 - 1 - \frac{10 \times 3}{100} \right) \]. Calculating the terms gives us \( 930 = P \left( 1.331 - 1 - 0.3 \right) \) and simplifying leads to \( 930 = P \times 0.031 \), which gives us \( P = \frac{930}{0.031} \approx ₹ 30000 \). So, the principal amount on which the interest difference occurs is approximately ₹ 30000. To make the topic even more fun, did you know that the concept of compound interest is often referred to as "interest on interest"? It's like a financial snowball effect where your money gathers momentum and grows faster the longer it's left to compound. This principle is why many people encourage early investing—the sooner you start, the more pronounced the compounding effect! Also, if you're curious about how these calculations came to be, many past scholars, including the great mathematician Leonardo da Vinci, recognized the power of compounded growth. Nowadays, there are not only traditional ways to calculate this but also numerous online calculators that provide instant results, reflecting how technology has made financial math more accessible!