Aptitude - Compound Interest - Discussion

As we know that,

The formula for annual compound interest, including principal sum, is:

A = P (1 + r/n) (nt).

Where:

A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for

C.I. when interest compounded yearly = Rs. 5000 * (1 + 4/100) * (1 + (4/2) /100)

= Rs.(5000 * 26/25 * 51/50) = Rs. 5304.

C.I. when interest is compounded half-yearly = Rs. 5000 * (1 + 2/100) 3
= Rs.(5000 * 51/50 * 51/50 * 51/50) = Rs. 5306.04,

Difference = Rs.(5306.04 - 5304) = Rs. 2.04.

Can someone please explain the calculation of C.I for yearly basis? I am not getting this.

1*1/2 means 3/2 means 18 months.

Calculate C.I. for half-yearly 3 times add them which will be 306.04.
Calculate C.I. for yearly then add the first half-yearly C.I. which will be 200+104 = 304.
Calculate the difference of both is 2.04.

I think the right Answer is 3.06.

We can do the same thing for both C.I.

We don't need to do extra stuff like 3/2 and all just try I got my answer correctly without using this method.

I too agree the answer is 3.06.

By the question;

CI yearly - CI half yearly.
P((1+R÷100)^n-1)- p((1+R÷200)^n)-1).
= 5000((1+4÷100)^3÷2-1)-5000((1+4÷200)^3-1).
= 306.04-302.98.
= 3.06.

When interest is compounded yearly then we calculate the time = 1 1/2.
When interest is compounded half-yearly, then we calculate the time = (1 1/2)/2 = 3/2*2=3.

Short cut method:
Rate given - 4%.
CI for yearly,
4%=1/25(first year).
2%=1/50(6 month)(rate divided by 2).

25:26.
50:51.
1250: 1326 //(25*50)and (26*51).
1250x=5000.

So x = 4,
CI = 1326*4 = 5304.

CI for half-yearly,
2% = 1/50(rate divided by 2).
50:51
50:51
50:51
125000:132651 //(50*50*50) and (51*51*51).

125000x = 5000.
x = 0.04.

So 0.04*132651=5306.04

So difference is 5306.04 - 5304=2.04(answer).

I didn't understand this, please explain me.