DIRECTIONSfor the question:Solve the following question.The difference between simple and compound interest (compounded annually) on a sum of money for 2 years at 10% per annum is Rs. 65. The sum is (in Rs.) (in numerical value)Correct answer is '6500'. Can you explain this answer?

Question

Answer

Using the formula of difference for 2 years

► P = D/(R/100)², where D= difference between simple and compound interest
► P = 65/(10/100)²
► P = Rs 6500

Answer

Let p=100
10. 10
1
diff=1=65
principal=100=6500

Answer

Calculation of Simple Interest:
Let the principal amount be P and the rate of interest be R. The simple interest for 2 years can be calculated using the formula:

Simple Interest = (P * R * T) / 100

Here, T = 2 years and R = 10% = 10/100 = 0.1

Calculation of Compound Interest:
The compound interest (compounded annually) for 2 years can be calculated using the formula:

Compound Interest = P * (1 + R)^T - P

Here, T = 2 years and R = 10% = 10/100 = 0.1

Difference between Simple and Compound Interest:
The difference between simple and compound interest is given as Rs. 65.

Compound Interest - Simple Interest = 65

(P * (1 + R)^T - P) - ((P * R * T) / 100) = 65

Simplifying the equation, we get:

(P * (1 + 0.1)^2 - P) - ((P * 0.1 * 2) / 100) = 65

(P * 1.1^2 - P) - (0.002P) = 65

(1.21P - P) - (0.002P) = 65

0.21P - 0.002P = 65

0.208P = 65

P = 65 / 0.208

P ≈ 312.5

Therefore, the principal amount is approximately Rs. 312.5.

Conclusion:
The sum of money, in numerical value, is Rs. 6500.

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