What is the difference between simple interest and compound interest?

You lend Rs.10,000 to a friend at 10% a year.

• With simple interest, your friend pays Rs.1,000 interest every year, always worked out on the original Rs.10,000.
• With compound interest, the first year's Rs.1,000 is added to the amount owed. The second year's interest is 10% of Rs.11,000, which is Rs.1,100. Interest earns interest.

This is why a fixed deposit or a SIP grows faster over long periods, and why unpaid credit card dues grow so quickly.

Question: Find the SI and CI on Rs.10,000 at 10% per annum for 2 years, and the difference between them.

Simple interest: SI = 10,000 x 10 x 2 / 100 = Rs.2,000.

Compound interest:

• After year 1: 10,000 x 1.1 = Rs.11,000.
• After year 2: 11,000 x 1.1 = Rs.12,100.
• CI = 12,100 - 10,000 = Rs.2,100.

Difference: 2,100 - 2,000 = Rs.100. Shortcut: P x (R/100)^2 = 10,000 x (10/100)^2 = 10,000 x 0.01 = 100.

const p = 10000;
const si = p * 10 * 2 / 100;
let amount = p;
for (let year = 1; year <= 2; year++) amount = amount * 110 / 100;
console.log(si); // Output: 2000
console.log(amount - p); // Output: 2100

• SI = P x R x T / 100, and amount = P + SI. It grows in a straight line.
• Compound amount A = P x (1 + R/100)^T, and CI = A - P. It grows faster each year.
• Compounded half-yearly: halve the rate and double the time periods. At 10% a year compounded half-yearly for 1 year, use 5% for 2 periods: 10,000 x 1.05 x 1.05 = Rs.11,025, so CI = Rs.1,025.
• Difference for 2 years: CI - SI = P x (R/100)^2.
• Difference for 3 years: CI - SI = P x (R/100)^2 x (3 + R/100).
• Year 1: SI and CI are always equal for the first year when interest is compounded yearly.

Bank fixed deposits, recurring deposits, home loans and education loans all use compound interest, usually compounded quarterly or monthly. Simple interest shows up in short-term loans and some informal lending. Bank PO, SSC and placement tests ask SI and CI almost every time.

• Using the SI formula for a CI question, or the other way round.
• Forgetting to change the rate and time when interest is compounded half-yearly or quarterly.
• Reporting the amount when the question asks for the interest. Subtract P.
• Writing the rate as 10 instead of 0.10 inside (1 + R/100).

• A sum doubles in 5 years at simple interest. What is the rate?
• A sum doubles in 4 years at compound interest. In how many years will it become 8 times?
• Find the difference between CI and SI on Rs.5,000 for 2 years at 8% per annum.
• What is the difference between CI and SI on Rs.10,000 at 10% for 3 years?