The difference between simple interest and compound interest on a certain sum of money for 2 years at 5% per annum is ₹10. Find the sum.

Question: The difference between simple interest and compound interest on a certain sum of money for 2 years at 5% per annum is ₹10. Find the sum.

• ₹2000
• ₹4000
• ₹6000 
• ₹7500 

Answer: 

 $$\mathrm{Formula \; \; \; :-\; P}=\frac{\text{Difference}\times {100}^2}{R^2}$$ $$P = \frac{10 \times 100 \times 100}{5 \times 5}$$ $$P = \frac{100000}{25}$$ $$P = 4000$$

Final Answer:

The sum is ₹4000.

Detail Solution:

Step 1: 

 Simple Interest Formula:

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

• $P$ = Principal (sum to be found)

• $R$ = Rate of interest = 5% per annum

• $T$ = Time = 2 years

$$SI = \frac{P \times 5 \times 2}{100} = \frac{10P}{100} = \frac{P}{10}$$

Step 2: 

The compound interest is calculated using:

$$CI = P \left(1 + \frac{R}{100}\right)^T - P$$

Substituting values:

 $$CI = P \left(1 + \frac{5}{100}\right)^2 - P$$ $$CI = P \left(1.05\right)^2 - P$$ $$CI = P (1.1025) - P$$ $$CI = 1.1025P - P = 0.1025P$$

Step 3: 

We are given that:

 $$CI - SI = 10$$ $$0.1025P - \frac{P}{10} = 10$$

Converting $\frac{P}{10}$ to decimal:

$$0.1025P - 0.1P = 10$$ $$0.0025P = 10$$ $$P = \frac{10}{0.0025}$$ $$P = 4000$$

** The sum is ₹4000.

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