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 $(1.0526)^4 = 1.2275$);
Answer & explanation
Correct answer: option 3
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%