What will be the difference between simple interest and compound interest at 4% per annum on a sum of ₹5000 after 3 years

Question: What will be the difference between simple interest and compound interest at 4% per annum on a sum of ₹5000 after 3 years ?

• 24.32
• 36.32
• 25 
• 30.24 

Answer: 

To find the difference between simple interest (SI) and compound interest (CI) at a rate of 4% per annum on a sum of ₹5000 after 3 years, we use the following formulas:

1. Simple Interest 

$$SI = \frac{P \times R \times T}{100}$$

$P = 5000$,
$R = 4\%$,
$T = 3$ years.

$$SI = \frac{5000 \times 4 \times 3}{100} = \frac{600}{100} = 600$$

2. Compound Interest :

$$CI=P{(1+\frac{R}{100})}^T-P$$ $$CI = 5000 \left(1 + \frac{4}{100} \right)^3 - 5000$$ $$CI = 5000 \left(1.04\right)^3 - 5000$$ $$CI = 5000 \times 1.124864 - 5000$$ $$CI = 5624.32 - 5000$$ $$CI=624.32$$

$$\text{Difference}=CI-SI=624.32-600=24.32$$

Additional Method :

 Difference=P×R21002×T(T−1)/2\text{Difference} = \frac{P \times R^2}{100^2} \times T (T - 1) / 2

For 3 years, a simple shortcut formula is:

$$\text{Difference} = \frac{P \times R^2}{100^2} \times 3$$

• Principal (P) = ₹5000
• Rate of Interest (R) = 4% per annum
• Time (T) = 3 years

 $$\text{Difference} = \frac{5000 \times 4^2}{100^2} \times 3$$ $$= \frac{5000 \times 16}{10000} \times 3$$ $$= \frac{80000}{10000} \times 3$$ $$= 8 \times 3$$ $$= 24$$

** The difference between CI and SI after 3 years is ₹24

If you find this content helpful, consider supporting us by clicking on any of the ads on this page.

Mock Test Click Here

Madhyamik Previous Year Solution Click Here

CBSE Class 10 History Notes Click Here

You Can Translate It In Your Language: