Compare simple and compound interest, and understand why compound interest grows faster over time.
With compound interest, each year's interest is added to the principal before the next year's interest is calculated — meaning you earn interest on your interest. This is different from simple interest, where interest is always calculated on the original principal.
₹5000 is invested at 10% per year, compounded annually. Find the amount after 2 years.
Year 1: 5000 + 500 = 5500. Year 2: 5500 + 550 = ₹6050
Why does compound interest grow faster than simple interest at the same rate?
Because compound interest is calculated on a growing principal each year, while simple interest is always calculated on the original amount only
Instead of calculating year by year, the formula A = P(1 + R/100)ⁿ gives the amount directly, where P is principal, R is the annual rate, and n is the number of years.
Find the amount on ₹4000 at 5% per year, compounded annually, for 2 years.
A = 4000 × (1.05)² = 4000 × 1.1025 = ₹4410
Find the compound interest on ₹4000 at 5% per year for 2 years (from the amount above).
CI = Amount − Principal = 4410 − 4000 = ₹410
1. ₹8000 is invested at 10% per year, compounded annually. Find the amount after 2 years by calculating year by year.
2. Find the amount on ₹6000 at 10% per year, compounded annually, for 2 years using the formula.
3. Find the compound interest on ₹6000 at 10% per year for 2 years.
4. ₹10000 is invested at 5% simple interest and ₹10000 at 5% compound interest, both for 2 years. Which earns more, and why?
5. Find the amount on ₹2000 at 20% per year, compounded annually, for 2 years.