Question

the difference between the compound interest and simple interest of the sum of rupees 15000 for 2 years in Rupees 96 what is the rate of interest

Answer 1

Let the rate of interest be r
Principle = Rs. 15000
Term = 2yrs

Compound Interest =
$15000(( {1 + r \div 100)}^{2} - 1)$

Simple interest = 15000×2×r/100 = 300r
So,

$15000(1 + (2r \div 100) + ( {r \div 100}^{2} ) - 1) \: - 300r \: = 96$
$300r \: + \: 15000 \times ( {r \div 100}^{2} )) \: - 300r \: = 96$
$15000 \times {(r \div 100)}^{2} = 96$

${r}^{2} = (96 \times 10000) \div 15000$
${r}^{2} = 64$
$r = 8$
Hence rate of interest = 8%