What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1,000 after 4 years?

Correct option is D

Given:

- Principal ( P ) = Rs 1,000

- Rate ( R ) = 10% per annum

- Time ( T ) = 4 years

We need to calculate the difference between compound interest (CI) and simple interest (SI).

Formula Used:

1. Simple Interest (SI):

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

2. Compound Interest (CI):

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

3. Difference:

Difference = CI - SI

Solution:

1. Calculate SI:

​$$\text{SI} = \frac{1,000 \times 10 \times 4}{100} = 400$$​​

2. Calculate CI:

​$$\text{CI} = 1,000 \left(1 + \frac{10}{100}\right)^4 - 1,000$$​​

​$$\text{CI} = 1,000 \left(1.1\right)^4 - 1,000$$​​

​$$1.1^4 = 1.4641$$​​

​$$\text{CI} = 1,000 \times 1.4641 - 1,000$$​​

CI = 1,464.10 - 1,000 = 464.10

3. Calculate the Difference:

Difference = CI - SI

Difference = 464.10 - 400 = 64.10

Answer:

D. Rs. 64.10