Question

Find the difference between the compound interest and simple interest on Rs 20,000 at 12% per annum for 3 years, the compound interest being payable annually.

Answer 1

Case I :
Here P₁ = Rs.20000 and r = 12%
So, Amount after 1 year 
= ${\displaystyle \text{P}(1+\frac{\text{r}}{100})}$

= ${\displaystyle 20000(1+\frac{12}{100})}$

= ${\displaystyle 20000\times \frac{112}{100}}$
= 22400
Thus, P₂ = Rs.22400 and r = 12%
Amount after 2 year
= ${\displaystyle \text{P}(1+\frac{\text{r}}{10})}$

= ${\displaystyle 22400(1+\frac{12}{100})}$

= ${\displaystyle 22400\times \frac{112}{100}}$
= 25088
Thus, P₃ = Rs.25088 and r = 12%
Amount after 3 year
= ${\displaystyle \text{P}(1+\frac{\text{r}}{100})}$

= ${\displaystyle 25088(1+\frac{12}{100})}$

= ${\displaystyle 25088\times \frac{112}{100}}$
= 28098.56
Hence, Amount = Rs.28098.56
Also, C.I.
= A - P
= Rs.28098.56 - Rs.20000
= Rs.8098.56
Case II :
Simple interest = ${\displaystyle \frac{20000\times 12\times 3}{100}}$
= 7200
Difference bertween C.I. and S.I.
= Rs.8098.56  - Rs.7200
= Rs.898.56.