A sum at compound interest amounts to ₹6,050 in 2 years and ₹6,655 in 3 years. Find the rate and the principal.

Under compound interest, each year's amount is the previous year's amount times a fixed multiplier. So the amount after year 3 divided by the amount after year 2 is exactly that multiplier. Once you have the rate, you can walk backwards from any known amount to the principal by dividing by the multiplier the right number of times.

Question: Amount = ₹6,050 after 2 years and ₹6,655 after 3 years at CI. Find R and P.

1. Year 3 interest = 6,655 - 6,050 = ₹605.
2. Rate = 605 / 6,050 x 100 = 10%.
3. 6,050 = P x (1.1)^2 = P x 1.21, so P = 6,050 / 1.21 = ₹5,000.

Check forwards: 5,000 to 5,500 to 6,050 to 6,655. Correct.

If the gap is more than one year, say amounts after 2 and 4 years, then the ratio equals (1 + R/100)^2 and you take a square root.

const r = (6655 - 6050) / 6050;
console.log(Math.round(r * 100)); // Output: 10
console.log(Math.round(6050 / 1.21)); // Output: 5000

• Treating it as simple interest and subtracting 2 x 605 from ₹6,050.
• Calculating the rate on ₹6,655 instead of ₹6,050.