1.Simple Interest (SI)
Simple Interest is calculated only on the original principal amount.
Formula:
SI = (P × R × T) / 100
Amount = Principal + Interest
Where:
P = Principal
R = Rate of interest per year
T = Time in years
Important Point:
The principal remains the same every year.
Used in:
Short-term loans and basic calculations.
2.Compound Interest (CI) – Meaning
Compound Interest is the interest calculated on the principal plus the interest already added in previous years.
In CI, the principal increases every year.
That is why the amount grows faster than Simple Interest.
Used in:
Bank deposits, investments, business loans, savings accounts.
3.Compound Interest 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
Amount = 10,000 × (1.10)^2
Amount = 10,000 × 1.21
Amount = 12,100
CI = 12,100 − 10,000
CI = 2,100
4.CI with Changing Rates
If the rate is different each year:
Amount = P × (1 + R1/100) × (1 + R2/100) × (1 + R3/100) …
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
Amount = 24,640
CI = 24,640 − 20,000
CI = 4,640
5.Time in Years and Months
If time is given in years and months:
Convert months into years:
Months = M/12
Formula:
Amount = P × (1 + R/100)^T × (1 + M × R / 1200)
CI = A − P
Note:
This method is used when interest is compounded yearly but time includes extra months.
6.Half-Yearly Compound Interest
When interest is compounded half-yearly:
Rate per half-year = R/2
Number of periods = 2 × T
Formula:
Amount = P × (1 + R/200)^(2T)
Example 3 – Half-Yearly CI
Q: 5,000 at 8% per year for 2 years, compounded half-yearly.
Solution:
Rate per half-year = 8/2 = 4%
Periods = 2 × 2 = 4
Amount = 5,000 × (1.04)^4
Amount ≈ 5,849.29
CI = 5,849.29 − 5,000
CI ≈ 849.29
7.Quarterly Compound Interest
When interest is compounded quarterly:
Rate per quarter = R/4
Number of periods = 4 × T
Formula:
Amount = P × (1 + R/400)^(4T)
Example 4 – Quarterly CI
Q: 6,000 for 1 year at 10%, compounded quarterly.
Solution:
Rate per quarter = 10/4 = 2.5%
Periods = 4 × 1 = 4
Amount = 6,000 × (1.025)^4
Amount ≈ 6,622.80
CI = 6,622.80 − 6,000
CI ≈ 622.80
8.Finding Principal from Amount
If Amount is given and Principal is unknown:
Formula:
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 × 1.331 = 9,261
P = 9,261 ÷ 1.331
P ≈ 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) gives higher CI.
c. Always adjust the rate and number of periods according to compounding frequency.
d. Solve step by step:
First find rate per period.
Then find number of periods.
Then calculate amount.
Finally subtract principal to get CI.
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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