How compound interest works, simple vs compound

Steps

1. For simple interest, multiply the principal by the rate and the years, then divide by 100: 1,00,000 × 10 × 5 ÷ 100 = ₹50,000.
2. For compound interest, write the rate as a decimal and divide by the times compounded a year, m.
3. Raise 1 plus that to the power m × t. Yearly at 10% for 5 years: 1.10^5 = 1.61051.
4. Multiply by the principal: 1,00,000 × 1.61051 = ₹1,61,051.
5. Subtract the principal to get the compound interest, ₹61,051, or use the compound interest calculator.

How often the interest is added

On ₹1,00,000 at 10% for 5 years the final amount is ₹1,61,051 compounded yearly, ₹1,62,889 half-yearly, ₹1,63,862 quarterly, ₹1,64,531 monthly and ₹1,64,861 daily.

More frequent compounding always helps a little, but the gains shrink quickly. The jump from yearly to quarterly is ₹2,811; from monthly to daily it is only ₹330.

The gap widens with time

At 8% for 3 years, ₹1,00,000 earns ₹24,000 as simple interest and ₹25,971 compounded yearly, a small difference. At 10% for 20 years the simple interest is ₹2,00,000, while compounding gives ₹6,72,750 in total, which means ₹5,72,750 of interest. Compounding is slow at first and then takes over.

Which one applies

Most savings, deposits and investments compound. Some short loans and a few bonds use simple interest. Loans compound against you when you do not repay on time, which is why an unpaid balance grows so fast. Check the terms to see which kind applies and how often it is added.