Aptitude - Compound Interest - Discussion

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.

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.

If calculated for half year we should take rate/200 right?

Then why rate/100 is taken?

2.04 is the right answer.

The yearly compound interest in traditional manner 1st 6mnths is 5000* 4/100 = 200. And 2nd 6months is 5200 * 4/100 = 208 the if we add both 200+208=408 how come it's 304?

Can anybody explain it?

C.I ON PER YEAR.

N=1,1/2 r=4%. P=5000.
1st year-- 5000 in 4% is = 200,
Next we need 1/2 year interest so r=4/2. R=2%,
Hence 5200 in 2% is = 204.
Hence interest is 200+100=304.

Then find half year interest.
N=3 i.e ::-:'(1*1/2 in 3 half year),
R=2 because (4%is full year but we need half yr),

5000 in 2% is =100,
5100 in 2%is =102,
5202 in 2%is =104.04,
Total = 306.04.

Hence(half year - 1year) = 306.04 - 304.
Ans = 2.04.

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.

The formula is amount=P+C. I.
Then if we have to find C. I mean, it should be like C. I=amount-P, right?
But here they didn't put 1, can someone teach me this part of thought?

Very good explanation, Thank you.

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.