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Home >> Simple Interest >> Compound Interest >>

Compound Interest by Direct and Shortcut Method

Calculate Compound Interest (half yearly) Calculate Compound Interest (Quarterly) Difference Compound Interest Yearly & Half Yearly Difference Compound Interest Yearly & Quarterly Difference Compound Interest Half Yearly & Quarterly

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.


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