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 |
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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.
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