1. Simple Interest (SI)
SI = (P × T × R) / 100
Principal remains the same each year
Amount = Principal + Interest
Used in short-term loans and simple calculations
2. Compound Interest (CI) – Meaning
CI = Interest on principal + accumulated interest
Principal increases each year
Amount grows faster than SI
Common in bank deposits, investments, business loans
3. CI – Formula (Yearly)
Amount (A) = P × (1 + R/100)^T
Compound Interest (CI) = A − P
Where:
P = Principal, R = Rate (% per year), T = Time in years
Example 1 – Yearly CI
Q: Find CI on ₹10,000 at 10% per year for 2 years.
Solution:
Amount = 10,000 × (1 + 10/100)^2 = 10,000 × 1.21 = 12,100
CI = 12,100 − 10,000 = 2,100
4. CI with Changing Rates
If rates are different each year:
A = P × (1 + R1/100) × (1 + R2/100) × …
CI = A − P
Example 2 – Different Rates
Q: ₹20,000 for 2 years, 10% first year, 12% second year.
Solution:
Amount = 20,000 × 1.10 × 1.12 = 24,640
CI = 24,640 − 20,000 = 4,640
5. Time in Years and Months
Convert months into years: M / 12
Amount = P × (1 + R/100)^T × (1 + M × R / 1200)
CI = A − P
6. Half-Yearly CI
Rate per half-year = R / 2
Number of periods = 2 × T
Amount = P × (1 + R/200)^(2T)
Example 3 – Half-Yearly CI
Q: ₹5,000 at 8% per year for 2 years, half-yearly.
Solution:
Rate per half-year = 8/2 = 4% = 0.04
Periods = 2 × 2 = 4
Amount = 5,000 × (1.04)^4 ≈ 5,849.29
CI = 5,849.29 − 5,000 = 849.29
7. Quarterly CI
Rate per quarter = R / 4
Number of periods = 4 × T
Amount = P × (1 + R/400)^(4T)
Example 4 – Quarterly CI
Q: ₹6,000 for 1 year at 10%, quarterly.
Solution:
Rate per quarter = 10/4 = 2.5% = 0.025
Periods = 4 × 1 = 4
Amount = 6,000 × (1.025)^4 ≈ 6,622.80
CI = 6,622.80 − 6,000 = 622.80
8. Finding Principal from Amount
P = A / (1 + R/100)^T
Example 5 – Find Principal
Q: Amount = ₹9,261 in 3 years at 10% yearly CI.
Solution:
P × (1.10)^3 = 9,261
P = 9,261 ÷ 1.331 ≈ 6,960
9. Key Points to Remember
a. CI grows faster than SI because interest is added to the principal each year
b. More frequent compounding (half-yearly, quarterly, monthly) → higher CI
c. Formula adjusts depending on time units and compounding frequency
d. Always calculate step by step: first find rate per period, then number of periods, then amount
10. Important Questions with solutions
Q1: Yearly Compound Interest
Q: Find CI on ₹12,000 at 5% per year for 3 years.
Solution:
Amount = 12,000 × (1 + 5/100)^3 = 12,000 × 1.157625 ≈ 13,891.50
CI = 13,891.50 − 12,000 = 1,891.50
Q2: Half-Yearly CI
Q: ₹8,000 at 6% per year for 2 years, half-yearly.
Solution:
Rate per half-year = 6/2 = 3% = 0.03
Periods = 2 × 2 = 4
Amount = 8,000 × (1.03)^4 ≈ 8,000 × 1.1255 ≈ 9,004
CI = 9,004 − 8,000 = 1,004
Q3: Quarterly CI
Q: ₹10,000 at 12% per year for 1 year, quarterly.
Solution:
Rate per quarter = 12/4 = 3% = 0.03
Periods = 4 × 1 = 4
Amount = 10,000 × (1.03)^4 ≈ 10,000 × 1.1255 = 11,255
CI = 11,255 − 10,000 = 1,255
Q4: CI with Different Rates
Q: ₹15,000 for 3 years at 10%, 12%, 8% for 1st, 2nd, 3rd year respectively.
Solution:
Amount = 15,000 × 1.10 × 1.12 × 1.08
Amount ≈ 15,000 × 1.10 = 16,500
16,500 × 1.12 = 18,480
18,480 × 1.08 ≈ 19,958.40
CI = 19,958.40 − 15,000 ≈ 4,958.40
Q5: Finding Principal from Amount
Q: Amount = ₹14,641 in 3 years at 10% yearly CI. Find principal.
Solution:
P × (1.10)^3 = 14,641
P = 14,641 ÷ 1.331 ≈ 11,000
Q6: CI for Months & Years
Q: ₹5,000 at 12% per year for 2 years and 6 months (2.5 years), yearly CI.
Solution:
Convert time = 2.5 years
Amount = 5,000 × (1 + 12/100)^2.5
1.12^2.5 ≈ 1.12^2 × 1.12^0.5 ≈ 1.2544 × 1.0583 ≈ 1.326
Amount ≈ 5,000 × 1.326 ≈ 6,630
CI ≈ 6,630 − 5,000 = 1,630
Q7: CI Comparison – Yearly vs Half-Yearly vs Quarterly
Q: ₹6,000 at 8% per year for 2 years, compare yearly, half-yearly, quarterly CI.
Solution:
Yearly: A = 6,000 × 1.08^2 = 6,000 × 1.1664 = 6,998.40 → CI = 998.40
Half-Yearly: Rate = 4%, periods = 4 → A = 6,000 × 1.04^4 ≈ 6,999.40 → CI ≈ 999.40
Quarterly: Rate = 2%, periods = 8 → A = 6,000 × 1.02^8 ≈ 7,009.70 → CI ≈ 1,009.70
Observation: More frequent compounding → higher CI
Q8: CI in Real-Life Context
Q: A bank offers 10% yearly CI. If ₹50,000 is deposited for 2 years, what is the total amount received at the end?
Solution:
Amount = 50,000 × (1 + 0.10)^2 = 50,000 × 1.21 = 60,500
CI = 60,500 − 50,000 = 10,500
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