Aptitude - Compound Interest - Discussion

First of all, we need to understand that first amount of 1600 for 1 year it is compounded half-yearly that means taking half of the interest for 2 years, and another amount is the only half year that is take half of the interest for one year, so finally, the total interest is; 5.0625 + 2.5 = 7.5625%.
So, 7.5625% of 1600 = 121.

A = P (1 + r/n) ^nt.

A = Final amount.
P = Initial principal balance.
R = Interest rate.
N = Number of times interest applied per time period.
T = Number of time periods elapsed.

raman has some amount which he invests in two different banks.the rate of interest in first bank is 10% is compounded yearly while the rate of interest in second bank is 15% compounded yearly .if he gets equal amount of interest after 2 years from both banks then the deposit in first bank is what percent of total original amount?

@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.

@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.

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

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 There is not provided with any information regarding the interest is withdrawn.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.

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.

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

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.