The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?
8
10
12
Cannot be determined
Explanation:
| $ \left[15000 \times\left(1 +\dfrac{R}{100} \right)^2- 15000\right]-\left(\dfrac{15000 \times R \times 2}{100} \right) $= 96 |
| $\Rightarrow$ 15000$ \left[\left(1 +\dfrac{R}{100} \right)^2- 1 -\dfrac{2R}{100} \right] $= 96 |
| $\Rightarrow$ 15000$ \left[\dfrac{(100 + R)^2 - 10000 - (200 \times R)}{10000} \right] $= 96 |
| $\Rightarrow$ R2 =$ \left(\dfrac{96 \times 2}{3} \right) $= 64 |
$\Rightarrow$ R = 8.
$\therefore$ Rate = 8%.