Aptitude - Compound Interest - Discussion

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

FV=P(1+r/n)^(nt)

FV = Future value of the deposit.
P = Principal or amount of money deposited.
r = Annual interest rate (in decimal form).
n = Number of times compounded per year (1 or 2 or 3... etc).
t = Time in years for which the money has been deposited.

Use this formula and you will get the answer.

Can someone tell me why have they considered 1600 value for the next 6 months (P) should be 1600 + Interest for the next half.

According to me itis given that compounded half yearly
So rate=5/2=2.5%
So first 6 months ci=1600*2.5/100=40
Now amount=1600+40=1640

Now 2nd 6 months ci=3240*2.5/100=81

So total ci = 80+40 = 121.