Compound Interest Compounded Annually


 
 
Concept Explanation
 

Compound Interest Compounded Annually

Definition:  Compound interest is calculated as a percentage as a total amount a the end of the previous compounding period. 

Formula:   

First Type:  F_{v} = P_{v}(1 + i )^{n}    , 

 where   F_{v}   =   Future Value 

               P_{v}   =  Present Value or Original Amount

               i     =   Annual Interest Rate as a Decimal

       (i + 1)  =  multiplier 

               n  =  number of years of investment 

Illustration:   What will Rs 5000 invested at 8% p.a compound interest amount to after 2 years ? 

Solution  :   An interest rate of 8% indicates that  i = 0.08. 

                   For 2 years  , n = 2  and so   F_{v} = P_{v}(1 + i )^{n}    =  Rs 5000 times  (1.08)^{2}   =  Rs 5832 

 

Second Type

To find interest only, we use

                           Compound interest = F_{v}   -    P_{v}     

Illustration:  How much interest is earned  according to the above example1  . 

 Solution :  interest earned = $ 5832 - $ 5000 =  $ 832  

now , To Find Compound Interest (CI) when Interest is Compounded Annually:

In such cases where interest is compounded yearly, the interest accrued during the first year is added to the principal and the amount so obtained becomes the principal for the second year. The amount at the end of the second year becomes the principal for the third year, and so on.

Illustration: Find the compound interest on Rs 25000 for 3 years at 6% per annum, compounded annually.

Solution: Principal for the first year = Rs. 25000.

Interest ;for; the; first; year = frac{25000;X;6;X;1}{100}= Rs. 1500.

Amount at the end of the first year = 25000 + 1500 = Rs 26500.

Principal for the second year = Rs. 26500.

Interest ;for; the; second; year = frac{26500;X;6;X;1}{100}= Rs. 1590.

Amount at the end of the second year = Rs 26500 + 1590 = Rs 28090.

Principal for the third year = Rs 28090.

Interest ;for; the; third; year = frac{28090;X;6;X;1}{100}= Rs. 1685.40

Amount at the end of the third year =  28090 + 1685.40 =  Rs 29775.40.

Therefore, compound interest =  29775.40 - 25000  = Rs 4775.40.

Compound Interest By Formula:

Amount= Principalleft [1+frac{Rate}{100} right ] ^{time}

Compound ;Interest= Amount- Principal

For the above example:

Principal = 25000

Rate= 6%

time= 3 years

Amount= Principalleft [1+frac{Rate}{100} right ] ^{time}

Amount= 25000left [1+frac{6}{100} right ] ^{3}

= 25000left [1+frac{3}{50} right ] ^{3}

= 25000left [frac{53}{50} right ] ^{3}

= 25000 X ; frac{53}{50};X; frac{53}{50};X; frac{53}{50}= frac{53;X;53;X; 53}{5}=frac{148877}{5}=29775.4

Therefore, compound interest =  29775.40 - 25000  = Rs 4775.40.

Sample Questions
(More Questions for each concept available in Login)
Question : 1

Find the compound interest when Principal = Rs 3000, Rate = 5 % per annum and time = 2 years

Right Option : C
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Explanation
Question : 2

A factory kept increasing its output by the same percentage every year.find the percentage,if it is known that the output doubled in the last two years:

Right Option : B
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Explanation
Question : 3

The difference between simple interest and C.I. at the same rate for Rs.5000 for 2 years in Rs.72. The rate of interest is?

Right Option : D
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Explanation
 
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