Aptitude - Compound Interest - Discussion

I am not at all able to understand the whole sum. Please, someone, help me.

As per formula, S=p*(1+r/200)^2n.Where r=rate of interest per annum. Why we have taken 5/200 there.

As they didn't give rate of interest they gave compound interest.

Thank you @Anusha.

The difference between simple interest and compound interest to be compounded annually from the annual interest rate of 16% for 2 years on a fixed amount is 320.

Please tell me why you have taken 5/2*100?

We use compound interest formula of half-year because the interest rate imposing on 1600 deposited on 1 Jan was only for 6 months.

A=p(1+R/100)n but why take 200 places of 100?

Why we are using half yearly formula in the first case taking n=1/2, and in the 2nd case taking n=1 but keeping R as R/2?

@Indhu.

1 July, it is 6th month of the year, where there's total 12 months in a year
so, it means half year(6/12=1/2).

Therefore, [1600 x (1+5/2*100)]^2n,
= [1600 x (1+5/2*100)]^2*1/2,
=[1600 x (1+5/200)].

Amount after 1 year on Rs. 1600 (deposited on 1st Jan) at 5% when interest calculated half-yearly.
=P(1+(R/2)100)2T=1600(1+(5/2)100)2*1=1600(1+140)2

Amount after 1/2 year on Rs. 1600 (deposited on 1st Jul) at 5% when interest calculated half-yearly.
=P(1+(R/2)100)2T=1600(1+(5/2)100)2*12=1600(1+140)

Total Amount after 1 year.
=1600(1+140)2+1600(1+140)=1600(4140)2+1600(4140)=1600(4140)[1+4140]=1600(4140)(8140)=41*81=Rs. 3321.

Compound Interest = Rs.3321 - Rs.3200 = Rs.121.