Aptitude - Compound Interest - Discussion

Now only I understood. Thanks anusha.

Thank you. Anusha.

The question is for one year. What if 5 years? please help me. I've got headache thinking about this topic.

You people might confused with the formulae and there of three formulaes where n represents exactly year i.e n=1 year, n=1/2 half year so on.,

Then another thing the three formulaes were having a much difference look at it as individual dont miggle those all three formulaes 2gether .

Ex: to calculate half year compund intrest u shoud go with the second one
don't bother about the duration here we are calculating C.I for every half yearly what ever the term it be either 1 year or 2 years u shud use the half year formulae for calculating that... look at it as very abstract.

CI is nothing but interest on interest.
so first find SI for 1600
so SI= (1600 * 5 * 1/2)/100 = 40
now total money is 1640 after 6 month. he again deposit 1600 rs so
now in july beginning total money is 1640 + 1600 = 3240 rs
again find SI = (3240 * 5 * 1/2)/100 = 81 rs

So total interest is = 81 +40 = 121 Rs ans.

Sateesh and Jyoti gave the nice explaination.

At the time of first deposit i.e on January 1st

Amount= p[1+(R/2)/100]^2(n)
here n is 1 year beginning of the year
so amount = 1600[1+(5/2)/100]^2
=1600[1+(5/200)]^2
=1600[1+(1/40)]^2
=1600[41/40]^2
=1681.

Secondly when he deposited its July i.e after 6 months
so n=half of the year=1/2

Amount=p[1+(R/2)/100]^2n n=1/2 year
=1600[1+(5/200)]
=1600[41/40]
=1640.

now add both amounts
1681+1640=3321
1600 deposited 2 times by the customer in a year therefore 1600*2=3200

gain => 3321-3200=121.

Best way was shows by Jyoti.... Kudos Jyoti... :)

From 1st Jan to next 1st Jan i.e n=1(12 months)
C.I.1= 1600[1+(5/2*100)]^(2*1)

Now from 1st July to 1st Jan i.e n=1/2(6 months)
C.I.2= 1600[1+(5/2*100)]^(2*1/2)

C.I.=C.I.1 + C.I.2

1600
Interest 5% in 6 month (1/2 of a year) = 5/100 * 1600 * 1/2 = 40
1640 + 1600 = 3240(principal + previnterest + new deposit)
5% of 3240 in next 6 month = 5/100 * 3240 * 1/2 = 81
End of year total = 3240 + 81 = 3321

Gain = total with interest - deposit = 3321 - 3200 = 121