Aptitude - Compound Interest - Discussion

C.P - S.I
[p(1-r/100)^n-p ]-[(P*R*N)/100] = 96.

Where,
p=1500, n=2, R=?, C.P and S.I difference is 96.

[15000(1-r/100)^2-15000 ]-[(1500*R*2)/100] = 96 ...(1).

Now, 15000 common in above so take it out,

15000[1(1-r/100)^2 - 1 ]-[(1*R*2)/100] = 96 ...(2).

Take L.C.M. we get,

15000[(100 + R)^2 - 10000 - (200 x R)/10000] = 96 ...(3).

Where (100 + R)^2 is like (a + b)^2 = (a^2 + b^2 + 2*a*b).

(100^2 + R^2 + 2*100*R) = (10000 + R^2 + 200R).

Sub (10000 + R^2 + 200R) in eqn(3) we get,

15000[ (10000 + R^2 + 200R) - 10000 - (200 x R)/10000] = 96.

15000[ (10000 + R^2 + 200R - 10000 - 200R) /10000] = 96.

Now 10000 and 200R is cancelled, remaining.

15000[ R^2 /10000] = 96.

[15000R^2/10000] = 96.

[15R^2/10] = 96.

divide by 5 we get,

[3R^2/2] = 96.

Now keep the R^2 in left hand side and move 3/2 to right side

R^2 = 96(2/3) // 96/3 = 32.

R^2 = 32*2.

R^2 = 64 // square root of 64 is 8.

R = 8%.

Simply, the solution is;

15000 * [{1+(r/100)}^2-1]-(15000 * 2 * r)/100 = 96,
=> 15000[{1+(r/100)}^2-1-(2 * r)/100]= 96,
=> 15000[1+(r^2)/10000-1] = 96 where [(a+b)^2-2ab = a^2 + b^2],

=> 15000[r^2/10000] = 96,
=> r^2 = 64,
=> r = 8.

We can directly do this by using the formula.
Difference between SI and CI for 2 years = principle *(Rate of Interest)^2
= P(R%)^2.

So here the difference is 96, principle=15000.
96 = 15000*(R/100)^2.
r = 8%.

@Anonymous

for C.I. formula is=>

p(1-r/100)^n-p

without subtracting, which amount we get is

"Principle amount+Interest"

so to get C.I. we have to subtract it..

Hi All ,

There is a shortcut method for this -

C.I. - S.I. = P*R^2/(100)^2.
so if we will put the values here it will be like this;
96 = 15000*R*R/10000,
64 = R*R,
So R =8.

In 4th step how they done R^2=64 ?

If we solve it there should be R^2-200R=64 and this is a quadratic equation. Can anyone explain me how to solve this equation ?

Difference between S.I and C. I is;
D = P(R/100) ^2,
96 =15000(R/100) ^2,
(96 * 2)/3 =R^2,
64 = R^2,
Ans. R = 8.

Can the difference be added to the principal to get the amount for compound interest formula?

And then by using CI formula rate can be calculated.

Hi guys,

I will tell you the simplest method for the difference between Si and Ci sums.

Use the formula:
Difference = P*(R^2)/100^2.

It's simply p(r/100)^2
p=1500,r=x,t=2yrs
Thus
15000(x/100)^2 it finally comes out like
x^2=64
x^2=8^2
x=8
Therefore rate=8%