Question

The difference between simple interest and compound interest on a certain principal for 2 years at 4% is Rs. 36. Find the principal.

Answer 1

We first find the simple interest and compound interest assuming the principal to be Rs. $x$. Then, find the difference between S.I. and C.I. Taking this difference for Rs. $x$ we can find the principal.
Let the principal $P=\text{Rs.}x,R=4\%$ and $N=2$ years.
Simple interest,
$I=\frac{P\times N\times R}{100}=\frac{x\times 2\times 4}{100}=Rs.\frac{8x}{100}$
Now compound interest is
$A=P{(1+\frac{R}{100})}^n=x{(1+\frac{4}{100})}^2=x(1.04{)}^2=(1.0816)x$ Rs.
Hence the compound interest $=1.0816x-x=0.0816x$.
Now, C.I. - S.I. $=0.0816x-\frac{8x}{100}=\frac{8.16x-8x}{100}=\frac{0.16x}{100}$
The difference in CI and SI is Rs. $0.16$ when the principal is Rs. $x$.
But the difference is Rs. $36$ then the principal is $x=\frac{100}{0.16}\times 36=22,500$. Thus the principal is Rs. $22,500$.