Aptitude - Compound Interest - Discussion

For 1/2 year formula is =P(1+(R/2)/100)^ 2n.
Now 1600 for 1st 1/2 year or 6 months so n=1/2.
=1600(1+(5/200)^1 = 1640.

This money bank won't returns him on July 1st it is kept in the bank till December. So from July to December 1640 also carries interest again apply formula for this with n=1/2
we get 1681 here 81 is the interest he got.

On July again he deposits 1600 again apply formula we get 1640 40 is the interest so total interest 81+ 40 = 121.

Hi, I don't understand how you set up the calculations in that way. The formula is fv=pv (1+r) n. Aren't the calculations suppose to be fv=1600 (1+0.05)1?

I did not understand the first calculative statement please help me.

Why [1600 x (1 + 5/2 x 100 )] this step is taken after the half-yearly count?

If haf yearly then n=2n and if for 2years then n=2n.

@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.

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?

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

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