Aptitude - Simple Interest - Discussion

The question said at the interest rate of 10% which probably means for 1year per annum, but he includes every 6 months interest. That means an interest rate of 6 months will become (5% half of 1 year) + another 6 months (5%half of 1year).

Now, using the effective rate of interest formula.
i,e (a + b + a * b/100),
(5+5 + 5 * 5/100)
(10 + 25/100),
(10 + 0.25),
(10.25) answer.

@All.

Here is the clarification.

(i) When "T" i.e., the time is given in months then it should be divided by 12 to convert into years.

(ii) When "T" i.e., the time is given in days then it should be divided by 365 to convert into years.

Why didn't we use (1+i)^n-1 here? Please explain.

Let the principal amount be x.
i.e p=x and rate of interest r=10.
and time = 1/2 (half year).

For first six months simple interest i = ptr/100.
=> i =((x )(1/2)(10))/100,

By solving above equation we get i= x/20,
Now new principal amount =x+(x/20) =>21x/20,
=>p=21x/20.

For second six months simple interest i= ptr/100.
=> i=( (21x/20)(10)(1/2) )/100.
=>i=21x/400.

Now total amount TA is = principal amount +interest on first six months +interest second six months.
=>TA=(x)+(x/20)+(21x/400).
=>TA=441x/400,

Now interest for 1 year is= total amount TA -actual principal amount.
ie. i= (441x/400)-x.
i= 41x/400.
Now for an effective rate of interest r.
i=ptr/100.
p=x,r=?,t=1(for complete 1 year),i=41x/400(interest for complete one year).
=> 41x/400=( (x)(1)(r) )/100.
=> r=41/4.
=> r=10.25.

The unit for rate of interest is P.C.P.A that is per-cent per annum, therefore we had calculated the effective rate of interest for 1 annum i.e. 1 year.

Question did not mention that the interest is to be calculated for 1 year only.

Total Simple Interest is Rs.5.00+5.25 = 10.25
How can we say that it is a rate of interest whereas it is formula of calulating simple int.

Why we take last 6 months principal as 105?

Because question suggests that "he includes the interest every six months for calculating the principal".

I did not get, how 10.25 is consider as rate not S.I. ?

Can anybody help me and Kiran ?