Aptitude - Compound Interest - Discussion

CI - SI = P(R/100)^2,
1 = P(4/100)^2,
1 = P(1/25)^2,
1 = P /625.
625 = P.

Hi.

Before solving this question you have to be aware on S.I and C.I formula's.

S.I = PTR/100.

Where as AMOUNT = P (1+ R/100) ^T ====> IN C.I.

AMOUNT = P + C.I.

C.I = P (1+ R/100) ^T - P.

In the question, they give the difference between S.I AND C.I is rupee 1.

First Calculate S.I.

Let the PRINCIPAL or SUM be ==> '' P '', TIME = 2, RATE = 4%.

S.I = PTR/100 ==> P*2*4/100 ==> 2P/25.

Now C.I = P (1+R/100) - P ==> P (1+4/100) - P ==> 51P/625.
51P/625 - 2P/25 = 1.
LCM IS 625.
51P - 50P/625 = 1.
P = 625.

I hope this will be helpful.

Thank you.

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

In C. I = where -x is come from? Please explain me.

Suppose that we take the sum 100.

2 years simple interest of 100 is 108.
And 2 years compound interest of 100 is;
108.16.

The difference between two interests is 108.16-108 = 0.16;
Now we can say that;
0.16 difference than 100 sum.

1 difference then what will be the sum?

Hence
0.16 : 100 :: 1 : ?
100×1
--------
0.16
= 10000/16.
= 625.

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.

SI = 8%.
CI = 8.16%.
CI - SI = 1.
8.16% - 8% = 1.
0.16% = 1.

Sum of the difference principal = 1/0.16 * 100 = 625.

@All.

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

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.