What is the difference between compound interest and simple interest on ₹5,000 for 2 years at 8% per annum?
₹32. For 2 years the difference is P x (R/100)^2 = 5,000 x 0.08 x 0.08 = ₹32. It is the interest earned in year 2 on year 1's interest.
Explain it simply
In the first year, simple and compound interest are identical. In the second year, compound interest also earns interest on the first year's interest, while simple interest does not. So the whole difference over two years is just "interest on the first year's interest", which is a small number you can compute in one line.
Example
Question: P = ₹5,000, R = 8%, T = 2 years. Find CI - SI.
- Year 1 interest = 8% of 5,000 = ₹400 (same for SI and CI).
- SI for 2 years = ₹800.
- CI: amount = 5,000 x 1.08 x 1.08 = ₹5,832, so CI = ₹832.
- Difference = 832 - 800 = ₹32.
Shortcut: P x (R/100)^2 = 5,000 x 0.0064 = ₹32. That is 8% of the first year's ₹400.
For 3 years the difference is P x (R/100)^2 x (3 + R/100) = 5,000 x 0.0064 x 3.08 = ₹98.56.
const P = 5000, r = 0.08;
console.log(Math.round(P * r * r)); // Output: 32
console.log((P * r * r * (3 + r)).toFixed(2)); // Output: 98.56What to say in the interview
"In year one they are equal; the gap is the interest on the first year's interest. For two years that's P times R over 100 squared, which is 32 rupees here."
Common mistakes
- Using the 2-year formula for 3 years.
- Forgetting to convert 8% to 0.08 before squaring.