Simple and Compound Interest
Core Concepts
1. Simple Interest (SI)
SI = P x R x T / 100
Amount = P + SI = P(1 + RT/100)
P = Principal, R = Rate per annum, T = Time in years.
2. Compound Interest (CI)
Amount A = P(1 + R/100)^T (compounded annually)
CI = A - P
Compounded half-yearly: A = P(1 + R/200)^(2T)
Compounded quarterly: A = P(1 + R/400)^(4T)
3. CI - SI Difference
For 2 years: CI - SI = P(R/100)^2
For 3 years: CI - SI = P(R/100)^2 x (R/100 + 3)
4. Effective Rate
Effective annual rate = (1 + r/n)^n - 1 (r = nominal rate, n = compounding periods per year)
5. Rule of 72
Money doubles in approximately 72/R years (at R% per annum compound interest).
Practice Problems
Q1: SI on Rs 5000 at 8% for 3 years?
SI = 5000 x 8 x 3/100 = Rs 1200.
Q2: CI on Rs 10000 at 10% for 2 years?
A = 10000(1.1)^2 = 12100. CI = 2100.
Q3: In what time does Rs 4000 become Rs 4800 at 10% SI?
SI = 800. 800 = 4000 x 10 x T/100 -> T = 2 years.
Q4: CI - SI difference for Rs 8000, 5% for 2 years?
CI - SI = P(R/100)^2 = 8000 x (0.05)^2 = 8000 x 0.0025 = Rs 20.
Previous Year Questions
SBI Clerk 2023: At what rate SI, Rs 2000 becomes Rs 2800 in 4 years?
SI = 800. 800 = 2000 x R x 4/100 -> R = 10% per annum.
IBPS PO 2022: CI on a sum at 20% for 3 years is Rs 728. Find sum.
728 = P[(1.2)^3 - 1] = P[1.728-1] = 0.728P -> P = Rs 1000.