A Car financier claims to be lending money at simple interest, but he includes…
2025
A Car financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 20%, the effective rate of interest becomes:
- A.
21.5%
- B.
21%
- C.
34.5%
- D.
32%
Attempted by 2 students.
Show answer & explanation
Correct answer: B
Step-by-Step Solution
Although the financier claims to be using simple interest, adding interest to the principal every six months effectively turns the transaction into compound interest, compounded semi-annually.
Understand the semi-annual rate:
Annual interest rate = 20%.
Since the interest is added every six months, we divide the annual rate by 2.
Interest rate per six months = 20% / 2 = 10%.
Calculate the growth over one year:
Let the initial principal be Rs. 100.
First six months: Interest = 10% of 100 = Rs. 10.
New principal after six months = 100 + 10 = Rs. 110.
Next six months: Interest = 10% of 110 = Rs. 11.
Total amount at the end of one year = 110 + 11 = Rs. 121.
Determine the effective rate:
The total interest earned over the year is Rs. 121 - Rs. 100 = Rs. 21.
Effective interest rate = (Total interest / Initial principal) * 100 = (21 / 100) * 100 = 21%.