Aptitude - Compound Interest - Discussion

Here, use a simple formula for the difference of 2 years = (pr) ^ 2/10000.

@All.

There is a direct formula to solve the difference between CI and SI is;
Difference = Principal * Rate^2 /100^2,
1 = P*16/10000,
10000/16 = P,
P = 625.

CI for 2 year, 4%=1/25.

25 26
25 26
--- ---
625 676

When P = 625 CI = 51.
Calculating SI When P = 625, T = 2,R = 4.
SI = 50.
CI-SI =1.
Condition is satisfying;
P must be 625.

@All.

Principle = difference(100/r)^2.
=> p = 1(100/4)^2 = (25)^2 = 625.

Profit of two is the same for C and S but it is a different profit of profit last year.

So, let first-year profit x then
4%of x = 1,
x= 25.
If.
Principle y.
Then 4%of y = 25,
y= 625.

The difference between S.I and C.I for two years is P.r^ 2/100^2.
Use this formula;
1 = p.4 * 4/100*100.
= 625 Answer.

we have difference formula for this question and that is;
CI - SI = P(R/100)^2,
1 = P(4/100)^2,
1 = P(1/25)^2,
1 = P /625.
625 = P.

So the reason CI is subtracted with P ([CI-P]-si) here is because;

CI calculates the amount after the principal has been compounded, that is it includes the compounded interest to the initial principal.

If the principal was 100 in this problem then CI would've been 108.16 (if I'm not wrong), which would include the interest (8.16) that has been added to the initial principal of 100.

So, yeah the formula for ci is more like 'compounded amount' (ca) rather than compounded interest. To find out exactly how much interest has been compounded you have to subtract 'ca' with the principal amount.

Explanation:
Let initial amount P = X.
R=4, T=2.
Now,
SI = P * R * T/100 = x * 4 * 2/100 = 2x/25.
SI = 2x/25.
CI = P[1+R/100]^T-x = x[1+4/100]^2-x.
= x[1+1/25]^2-x,
= x[26/25]^2-x,
= x[676/625]-x,
=676x/625-x,
=676x-625x/625,
=51x/625,
CI = 51x/625.

According to the question.
CI-SI = 1.
51x/625 - 2x/25 = 1.
51x-50x/625 = 1.
X = 625
So, P = 625.

Let the sum be Rs. x.
Then,
ci = (x(1 + r/100)^n - x ) why subtracting with x again?