Sunil and Kamal took loan of ₹40,000 each for 1 year 6 months from a moneylender who charged simple interest from Sunil 11% per annum and compound interest from Kamal 10% per annum compounded semi-annually. Who paid more interest and by what amount?

Correct option is B

Given:

Loan Amount = ₹40,000

Time = 1 year 6 months = 1.5 years

Sunil: Simple Interest 11% p.a.

Kamal: Compound Interest 10% p.a., compounded semi-annually

Formula Used:

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

Compound Interest (CI) = A - P, where$$A = P \left(1 + \frac{R}{n \cdot 100}\right)^{nt}$$​​
(n = number of times interest is compounded per year)

Solution:

SI= $$\frac{40000 \times 11 \times 1.5}{100} = ₹6600$$​​

For CI:

P = ₹40,000, R = 10%, n = 2 (half-yearly), t = 1.5 years → nt = 3

​$$A = 40000 \left(1 + \frac{10}{2 \times 100} \right)^3 = 40000 \left(1 + 0.05\right)^3 = 40000 \times (1.157625) = ₹46,305$$​​

CI = A - P = 46,305 - 40,000 = ₹6,305

Sunil paid interest = ₹6,600

Kamal paid interest = ₹6,305

Difference = ₹6,600 - ₹6,305 = ₹295

Sunil paid ₹295 more interest than Kamal.