Simple, Compound and Rate of Interest with Examples

Example 1
A customer deposits an amount of 100 $ in the bank.
So, 100 $ is the principal.

Example 2
The money borrower borrows an amount of 200 $ from the money lender.
So, 200 $ is the principal.

Example 1
The bank adds 20 $ to the customer's deposited amount of 100 $.
So, 20 $ is the interest given by the bank to the customer.

Example 2
The money borrower gives back to the money lender an extra 40 $ in addition to the borrowed 200 $.
So, 40 $ is the interest paid by the money borrower to the money lender.

Example 1
The bank gives interest of 20 $ on the customer's deposited principal amount of 100 $.
Amount = Principal + Interest
∴, Amount = 100 + 20 = 120
So, amount in customer's account after receiving the interest = 120 $.

Example 2
The money borrower gives back to the money lender an extra 40 $ in addition to the borrowed 200 $.
Amount = Principal + Interest
∴, Amount = 200 + 40 = 240
So, the amount of money returned back by the borrower = 240 $.

Example 1
A sum of $1000 is lent for 2 years at the rate of 5% per annum. Find the simple interest.
Principal = 1000
Rate of interest = 5% per annum
Time = 2 years
$\text{SI}=\frac{\text{P}\times \text{R}\times \text{T}}{100}$
$=\frac{1000\times 5\times \text{2}}{100}$
= 100 $

Example 2
Find the amount paid by a farmer if he borrows $2400 for the time of 4 years at the rate of 6% per annum.
Principal = 2400
Rate of interest = 6%
Time = 4 years
$\text{SI}=\frac{\text{P}\times \text{R}\times \text{T}}{100}$ $=\frac{2400\times 6\times \text{4}}{100}$
= 576
Amount = Principal + Interest
Amount = 2400 + 576
= 2976 $

Calculate compound interest on Rs 6000 for 3 years at 2% per annum.
Method 1
P = 6000
R = 2% per annum
T = 3 years
As we know, $A=P{(1+\frac{R}{100})}^{\mathrm{n}}$
$=6000{(1+\frac{2}{100})}^3$
$=6000{\left(\frac{\mathrm{100\; +\; 2}}{100}\right)}^3$
$=6000{\left(\frac{102}{100}\right)}^3$
A = 6367.248
CI = 6367.248 - 6000
CI = 367.248

Method 2
P₁ = Principal for first year = Rs 6000
T = 1 year
R = 2% per annum
Interest at the end of first year $=\frac{\mathrm{6000\; \times \; 2\; \times \; 1}}{100}$ = 120
Amount at the end of first year = 6000 + 120 = 6120
P₂ = Principal for second year = Rs 6120
T = 1 year
R = 2% per annum
Interest at the end of second year $=\frac{\mathrm{6120\; \times \; 2\; \times \; 1}}{100}=\frac{1224}{10}$ = 122.4
Amount at the end of second year = 6120 + 122.4 = 6242.4
P₃ Principal for third year = Rs 6242.4
T = 1 year
R = 2% per annum
Interest at the end of third year $=\frac{\mathrm{6242.4\; \times \; 2\; \times \; 1}}{100}$
= 124.848
Amount at the end of third year = 6242.4 + 124.848 = 6367.248
Compound interest = Final amount - Original principal
=6367.248 - 6000
=367.248
In the above example, we can also find compound interest by adding interest for consecutive years.
CI = interest of Ist year + interest of 2nd year+ interest of 3rd year
= 120 + 122.4 + 124.848
= 367.248

Calculate simple interest and compound interest for $3000 at 4% per year in 3 years.

Simple interest calculations
Principal = 3000
Rate of interest = 4%
Time period = 3 years
$\text{Simple interest}=\frac{\text{P}\times \text{R}\times \text{T}}{100}$
$=\frac{\mathrm{3000\; \times \; 4\; \times \; 3}}{100}$
$=\frac{36000}{100}$
= 360
Compound interest calculations
$A=P{(1+\frac{R}{100})}^{\mathrm{n}}$
$=\mathrm{3000}{(1+\frac{4}{100})}^3$
$=3000{\left(\frac{\mathrm{100\; +\; 4}}{100}\right)}^3$
$=3000{\left(\frac{104}{100}\right)}^3$
$=3000\times \frac{104}{100}\times \frac{104}{100}\times \frac{104}{100}$
$=\frac{3374592000}{1000000}$
= 3374.592
Compound interest = amount - principal
= 3374.592 -3000
= 374.592
To understand this concept more briefly, lets have a look at the following tables with year wise calculations.

Difference between simple interest and compound interest
Simple interest for 3 years = 120 + 120 + 120 = 360
Compound interest for 3 years = 120 + 124.8 + 129.792 = 374.592
Difference between them = 374.592 - 360 = 14.592