Question

if the difference between the simple interest and compound interest compounded annually on a certain sum for two years at 5% rate of interest is rupee 1,then the sum is

Answer 1

Let the sum = P
The simple interest on the sum for 2 years = 2 * 0.05P
If the sum has interest compounded for 2 years, the total amount of the sum and the interest is given by
\[A=P(1+0.05)^{2} .........(1)\]
The compound interest on the sum for 2 years is therefore
\[1.05^{2}P-P=P(1.05^{2}-1)=0.1025P\]
The difference between the amounts of compound interest and simple interest is given by
\[0.1025P-0.1P=0.0025P=1\ rupee\]
Therefore the sum P is found from:
\[P=\frac{1}{0.0025}\ rupees\]