Simple and Compound Interest
Simple and Compound Interest
This domain tests interest on a principal over time. Simple interest (SI) is fixed on the original principal each year; compound interest (CI) is added to the principal, so later interest is calculated on a larger amount.
Core rules
- SI = P × R × N / 100, where P is principal, R is rate per annum, N is time in years. Amount A = P + SI.
- Compound amount A = P(1 + R/100)^N; CI = A − P.
- For half-yearly compounding, halve the rate and double the number of periods: use R/2 and 2N.
- For two years, CI − SI = P(R/100)². This shortcut applies only to two years at the same rate.
Worked example
Find SI and CI on ₹8,000 at 10% p.a. for 2 years. SI = 8000 × 10 × 2 / 100 = ₹1,600. CI: A = 8000(1 + 10/100)² = 8000 × 1.21 = ₹9,680, so CI = ₹1,680. Difference = ₹80, which also equals 8000 × (10/100)² = 8000 × 0.01 = ₹80.
Traps
- Use R as a number, not a decimal: 10% means R = 10 in the formula.
- Time must be in years; 6 months = 0.5 year for SI.
- CI is not the same each year: year 1 interest is ₹800, year 2 is ₹880 in the example.
- Do not use the two-year difference shortcut for three years.