A person has taken a loan of Rs. 40,000 for 3 months from a lender who has deducted Rs.2,000 as interest at the time of lending. Then the effective rate of interest charged per annum by lender is (given $(1.0526)^4 = 1.2275$);

22.75%

The correct answer is Option (3) → 22.75%

Loan taken = Rs. 40,000

Interest deducted in advance = Rs. 2,000

So, net amount received = Rs. 40,000 − Rs. 2,000 = Rs. 38,000

At the end of 3 months, borrower repays = Rs. 40,000

Thus, effective interest for 3 months = 40,000 − 38,000 = Rs. 2,000

Effective rate for 3 months = $\frac{2000}{38000} = 0.05263 = 5.263\%$

Now, annual effective rate = $(1+0.05263)^4 -1$

= $1.0526^4 -1 = 1.2275 -1 = 0.2275$

= $22.75\%$

Effective annual rate of interest = 22.75%