Use the compound interest formula A=P(1+r/100)ⁿ directly, and apply it to real financial problems including depreciation.
A=P(1+r/100)ⁿ, where P is principal, r is rate per annum, and n is number of years. This avoids calculating year by year.
Find the amount on ₹15,000 at 10% per annum compound interest for 3 years using the formula.
A=15000×(1.1)³=15000×1.331=₹19,965
Find the compound interest on ₹20,000 at 5% per annum for 2 years.
A=20000×(1.05)²=20000×1.1025=₹22,050; CI=₹2,050
Depreciation reduces a value each year by a fixed percentage, using the same formula but subtracting: A=P(1−r/100)ⁿ.
A machine worth ₹50,000 depreciates by 10% per annum. Find its value after 2 years.
A=50000×(0.9)²=50000×0.81=₹40,500
Why does depreciation use (1−r/100) instead of (1+r/100)?
Because the value decreases each year rather than increases, so we subtract the rate instead of adding it
1. Find the amount on ₹10,000 at 10% per annum compound interest for 3 years.
2. Find the compound interest on ₹25,000 at 4% per annum for 2 years.
3. A car worth ₹6,00,000 depreciates by 15% per annum. Find its value after 2 years.
4. Find the amount on ₹8,000 at 5% per annum compound interest for 3 years.
5. A population of 40,000 grows at 5% per annum. Find the population after 2 years.