Aptitude - Compound Interest - Discussion

See the question it is given as half yearly so we should taken as n = 2.

Why n is taken as n=2?

For half yearly formula is:
amt= P+ (1+r/2/100)^ 2N

Considering half yearly, N=1/2 then value of 2N = 2* 1/2=1.

Why n=2?

For half yearly n should be 1/2.

How to get Rs100(p=100)?

Suppose i am taking Rs200 or 300. I am not getting the answer.

Can you explain it please?

I still don't understand what is n=? In this formula for calculating compound interest half year.

A = P[1+R/200]^2n.
Is it the no of slots like n=2 for 1 year, because Two six months slots(6 months+ 6 months).
Or is it n=1/2 because it is half of 1 year.

Please explain it clearly.

How n=1? for half year n=1/2 means 2n=2*1/2 it gives 1 right?

Half yearly calculation is not correct.

As for half yearly, Amount = P[1+R/100]2N; so for this context, it seems to be 1, if half yearly (2*1/2=1).

How is it possible to give the time still as 2 years?

Please explain.

Thank you.

@Durga.

There is no 106.09-106.

There's 106.09-100=6.09.

Let principal, P be Rs.100

Amount after 1 year on Rs.100 at 6% per annum when interest is compounded half-yearly

=P(1+(R/2)/100)^2T,
=100(1+(6/2)/100)^2*1,
=100(1+3/100)^2,
=100(103/100)^2,
=100*103*103/100*100,
=103*103/100,
=106.09.

This means, if interest is compounded half-yearly at 6%, Rs.100 becomes Rs.106.09 after 1 year

Now, we need to find out the rate of interest on which Rs.100 becomes Rs.106.09 after 1 year.

when the interest is compounded annually

P(1+R/100)^T=106.09
100(1+R/100)^1=106.09
100(1+R/100)=106.09
100+R=106.09
R=106.09/100=6.09%.

i.e, effective annual rate of interest is 6.09%

R=6% for normal 1 year,
R=3% for half yearly,
Effective percentage formula=R+R+(R*R)÷100,
ANS is 6.09.