Find the compound interest in 2 years after calculating simple interest

Solution:

Here,

In the first case,
Principal (P) = Rs. 150000
Time (T) = 5 years
Simple amount (A) = Rs. 252600
Rate of interest (R) = ?

We know, 

Simple Interest (I) = Simple Amount (A) - Principle (P) 

  = Rs. 252600 -Rs. 150000
  = Rs. 112500

Now, using formula for simple rate (R)

R = \(\frac{I\times100}{P\times T}\)
= \(\frac{112500\times100}{150000\times5}\)
= \(\frac{1125}{75}\)
= 15

∴ Rate of simple interest (R) = 15% p.a. (per annum)

Again, according to the second condition,

Rate of interest (R) = 15% p.a,
Time (T) = 2 years,
Compound amount (CA) = Rs. 198375,
Principal (P) = ?

By formula,

\(CA=p\left(1+\frac R{100}\right)^T\)
Or, \(198375=p\left(1+\frac{15}{100}\right)^2\)
Or, \(198375=p\left(1+0.15\right)^2\)
Or, \(198375=p\left(1.15\right)^2\)
Or, \(198375=1.3225P\)
Or, P = 150000

Hence principal (P) is Rs 150000 is the required answer.