Sunil's Simple Interest Calculation

The principal amount (P) is ₹40,000.

The rate of simple interest (R) is 11% per annum.

The time period (T) is 1 year 6 months, which is equal to 1.5 years.

The formula for Simple Interest (SI) is:

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

Plugging in the values:

$ \text{SI}_{\text{Sunil}} = \frac{40000 \times 11 \times 1.5}{100} $

$ \text{SI}_{\text{Sunil}} = 400 \times 11 \times 1.5 = 6600 $

Sunil paid ₹6,600 as simple interest.

Kamal's Compound Interest Calculation

The principal amount (P) is ₹40,000.

The annual interest rate is 10%.

Interest is compounded semi-annually, meaning twice a year (n=2).

The interest rate per compounding period (r) is $\frac{10\%}{2} = 5\% = 0.05$.

The time period (T) is 1 year 6 months, which is 1.5 years.

The total number of compounding periods (nt) is $2 \times 1.5 = 3$.

The formula for the Amount (A) in compound interest is:

$ A = P(1 + r)^{nt} $

Substituting the values:

$ A = 40000 \times (1 + 0.05)^3 $

$ A = 40000 \times (1.05)^3 $

$ A = 40000 \times 1.157625 = 46305 $

The Compound Interest (CI) is calculated as Amount - Principal:

$ \text{CI}_{\text{Kamal}} = 46305 - 40000 = 6305 $

Kamal paid ₹6,305 as compound interest.

Comparison of Interest Paid

Sunil's simple interest = ₹6,600

Kamal's compound interest = ₹6,305

To find who paid more, we compare the amounts:

₹6,600 > ₹6,305

The difference in interest paid is:

$ \text{Difference} = 6600 - 6305 = 295 $

Therefore, Sunil paid more interest than Kamal by ₹295.