Aptitude - Compound Interest - Discussion

How come 2*100?

Please explain me.

Jan= 1600 deposited.
Jan to july =6 month interest= 2.5% of 1600= 40.
July to dec = 2.5% of 40+ 40 = 41.

total interest on amount 1600 deposited on january= 40+41=81.

So, the interest on amount 1600 deposited on july = 40

Then, total interest = 40+81=121.

I am not getting how time be 2? Please explain.

1 year -->5%.
1/2 year -->2.5%.

At jan 1st=Rs.1600 --> 1600+(2.5% of 1600)=1600+40 = 1640.

At july 1st = Rs.1600+Previous amount + (2.5% of previous total) = 1600 + 1640 + (2.5% of(1600 + 1640)).
= 3240+81
= 3321----->At year last.

Total spent is 1600 + 1600 = 3200,
Threfore 3321 - 3200 = 121.

If on calculating the first 6 months then from July it is CI for both. Why only SI is considered in both time.

Ist half interest =1600*1/40 = 40,
IInd half interest/(1600+1600) * 1/40 = 80,
interest on Ist half intrest = 40 * 1/40 = 1,
Total CI= 40+80+1 = 121.

Amount from 1st January to 1st July is
Amount= 1600[1+5/(2*100)]^2.
= 1681.

Note: The principal amount becomes 1681 instead of 1600 because the money is deposited in the bank. There is not provided with any information regarding the interest is withdrawn.

So, the new principal amount at 1st July is 1600+1681 = 3281.
The amount at the end of the year becomes;
=3281[1+5/(2*100)]^2,
=3447.1.
The gain is =3447.1-3200.
=247.1 Rs.

Correct me, whether it is wrong.

I want to ask that, there is a 5% interest on every half a year, why you are calculating 5% interest for a year?

@Anom.

You are right but just once again read the 2nd line of the question.

It is being said that the amount is received in 1st of Jan and 1st of July which are basically half years in simple words - from 1st of Jan to 1st of July it's 6 months which is a half year and same way from 1st of July to 1st Jan is another 6 months which is another half year.

Therefore, the 5% of interest is calculated in Jan and July separately [ p- (1+r/100) ^t + p- (1+r/100) ^t] - p. Which calculated in half year basis only not for a year.

@All.

It's simple, first one is deposited on jan, the year n is 1, second one deposited on July which is half of one year, so year n is 1/2, just put this in the formula for compound interest half yearly you can get the answer.