In general, we can say that:
In Compound Interest , interest is calculated on the amount of previous year
Or we can also that:
In Compound Interest , interest is added after every one year to form a new principal.
Observe the following table:
1st Year calculations  Principal  $10,000  Interest charges @ 10% per annum  $1,000  Amount (Principal + Interest)  $11,000 
 2nd Year calculations  New Principal ( Amount of 1st year)  $11,000  Interest charges @ 10% per annum  $1,100  Amount (Principal + Interest)  $12,100 
 3rd Year calculations  New Principal ( Amount of 2nd year)  $12,100  Interest charges @ 10% per annum  $1,210  Amount (Principal + Interest)  $13,310 

Above table 1 represent calculation of Amount when interest is compounded annually . Also you can see that amount in the end of 1st years becomes principal for new year and so on..
Now since we got Amount = $13310
So, let’s find the compound interest using formula:
Compound Interest = Amount  Principal
Put values from the above table and we get:
CI = $13310  $10000
CI = $3310
In Table 1, you can see its very time consuming and long method to find amount. Therefore you can use following direct formula:
Direct Formula to Calculate Amount in case of compound interest:
Amount = P ( 1 + R / 100 ) ^{ T }
Here:
P is Principal
R is Rate of Interest
T is Time in years
Example : Find Compound interest on $10000 for 3 years at rate 10% interest per annum compounded annually.
Solution: As per the given question:
Principal or P = $10000
Rate of Interest or R = 10%
Time or T = 3 years
Apply formula to Calculate Amount:
Amount = P ( 1 + R/100 )^{ T }
Put values of P, R and T from above and we get:
= 10000 (1 + (10/100)^{ 3 }
Solve brackets by LCM method as shown in below steps:
= 10000 [(100 + 10) / 100]^{ 3 }
= 10000 (110 / 100)^{ 3 }
= 10000 (11 / 10)^{ 3 }
Expand the exponential form and we get:
= 10000 (1331 / 1000)
Solve the cross multiplication expression and we get:
= 13310
Therefore, amount is $13310
Now, apply formula to find compound interest:
Compound Interest = Amount – Principal
CI = 13310 – 10000
CI = 3310
Hence, compound interest is equal to $3310.
(you can match answer with the method used in table 1)
Shortcut Method to find Compound Interest
CI = P [ ( 1 + R / 100 ) ^{ T }  1]
Here:
P is Principal
R is Rate of Interest
T is Time in years
With this shortcut formula, you can directly calculate compound interest rather than first calculating Amount and then calculating compound interest.
Example : Find Compound interest on $10000 for 3 years at rate 10% interest per annum compounded annually.
Solution: As per the given question:
Principal or P = $10000
Rate of Interest or R = 10%
Time or T= 3 years
Apply above mentioned shortcut formula to calculate Compound Interest:
CI = P [ ( 1 + R/100 )^{ T }  1]
Put values of P, R and T from above and we get:
CI = 10000 [ ( 1 + 10/100 )^{ 3 }  1]
Solve brackets as shown in the below steps:
CI = 10000 [ { (100 + 10) / 100 }^{ 3 }  1 ]
CI = 10000 [ { 110 / 100 }^{ 3 }  1 ]
CI = 10000 [ { 11 / 10 }^{ 3 }  1 ]
CI = 10000 [ 1331 / 1000  1 ]
CI = 10000 [ (1331 1000) / 1000 ]
CI = 10000 [ 331 / 1000 ]
CI = 3310
Hence, compound interest is equal to $3310.

