Aptitude - Compound Interest - Discussion

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 think the right Answer is 3.06.

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.

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

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 we take time (n) in fraction as 3/2 in the yearly formula?

Please explain me.

Since compound interest (CI= p(1+(1/2)/100)}] ^2n for half year

Thus:

CI= 5000[1+{(4/2)/(100)}]^(2*(3/2)]
= 5000[1+{2/100}]^(3).
= 5306.04.

The issue is for 1 year.
I can understand the time n =1 but isn't it suppose to be 2x1 (2xn) for a half year but instead, they are taking 1 (1/2), which means they are taking a period of 1 and half years for calculating half-year compound interest.

Very good explanation, Thank you.

It's actually simple if you look at this in a different way.
The first CI on 4% per annum on 5000 is 200.
And for the next 6 months, it is 2% of 5200 so that's 102.
So,
Total is 200+104 = 304.

On the second case, it's taken half yearly so 2% every 6 months then put the value;
100 in the first 6 months.
102 in the next 6 months.
On the third 6 month, it becomes
2% of 5222.
ie 52.2 + 52.2 = 104.4,
100 + 102 + 104.4 = 306.4,
304 - 306.4 = 2.04.