Profit and Loss

Simple Interest is the interest calculated on the original amount (principal) for a specific period of time. It is calculated uniformly and does not change over time.

Formula:

SI = \frac{P \times R \times T}{100}

Where:

P

= Principal (amount borrowed or invested)

R

= Rate of interest (per year)

T

= Time period (in years)

Example:
Calculate the simple interest on Rs. 1000 at 5% per annum for 2 years.
Solution:

P = 1000

R = 5 %

T = 2

years

SI = \frac{1000 \times 5 \times 2}{100} = 100

Therefore,

SI = Rs. 100

Tips and Tricks:
1. Always convert the time period into years if given in months or days.
2. If the rate is given for a shorter period (e.g., 6 months), adjust it to a yearly rate.
3. Use the formula directly for quick calculations.

Compound Interest (CI)

Compound Interest is the interest calculated on the principal and the accumulated interest of previous periods. It grows faster than simple interest.

Formula:

A = P {(1 + \frac{R}{100})}^{T}

CI = A - P

Where:

P

= Principal

R

= Rate of interest (per year)

T

= Time period (in years)

Example:
Calculate the compound interest on Rs. 100 at 10% per annum for 3 years.
Solution:

P = 100

R = 10 %

T = 3

years

A = 100 {(1 + \frac{10}{100})}^{3} = 100 \times 1.331 = 133.1

CI = 133.1 - 100 = 33.1

Therefore,

CI = Rs. 33.1

Tips and Tricks:
1. For quick calculations, learn the values of

{(1 + \frac{R}{100})}^{T}

for common rates and time periods.
2. Use the formula for annual compounding. For other compounding periods (e.g., half-yearly), adjust the rate and time.
3. Remember that CI is always greater than SI for the same rate and time.

Formulas and Shortcuts

Important Points

MCQ Questions

Concept	Formula
Simple Interest	$SI = \frac{P \times R \times T}{100}$
Compound Interest	$A = P {(1 + \frac{R}{100})}^{T}$ , $CI = A - P$
Amount (Simple Interest)	$A = P + SI$
Amount (Compound Interest)	$A = P {(1 + \frac{R}{100})}^{T}$

1. What is the simple interest on Rs. 5000 at 8% per annum for 3 years?
a) Rs. 1000
b) Rs. 1200
c) Rs. 1500
d) Rs. 2000
Answer: b) Rs. 1200

2. If the compound interest on Rs. 1000 at 10% per annum for 2 years is:
a) Rs. 210
b) Rs. 220
c) Rs. 230
d) Rs. 240
Answer: a) Rs. 210

3. The difference between CI and SI on Rs. 2000 at 5% per annum for 2 years is:
a) Rs. 5
b) Rs. 10
c) Rs. 15
d) Rs. 20
Answer: b) Rs. 10

Simple Interest and Compound Interest

Simple Interest (SI)

Compound Interest (CI)

Formulas and Shortcuts

Important Points

MCQ Questions