Aptitude - Compound Interest - Discussion

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?

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.

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.

@ALL.

An explanation for why there is square in 1 st term in amount.

As there is square in first term amount indicating the duration because the CI given here is the half-yearly basis not yearly so from,

1 st Jan -1st Jan(next year)=1 year =2 half year.n=2
1st Jul- 1st Jul(next year)=6 months=1 half-year ie.n=1

1st 6th month (1jan to 1 July) (half-yearly basis) Rate of intrest=R/2 and R = 51.
Then interest =1600 X 5/2 X 100=>40.

Amount of 1st 6th Month = 1600(principal) + 40(interest) => 1640.
Same for july to dec now P=1640 and R = 5/2.
Then intrest =1640 X 5/2 X100==>41.

Amount of 2nd 6th Month=1640(principal)+41(interest)=>1681
then total amount with intrest = 1640+1681;
= 3321;

Toal amount gained = 3321 - (1600+1600).
= 121;

Well explained @Satheesh.

Thanks @Mohsin Khan.

Good, thanks @Mohsin Khan.

Yes right, Thanks @Amazu.