If a moneylender charges 'interest' at the rate of 10 rupees per 100 rupees per half year, payable in advance, then the effective rate of interest per annum is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 23.45%
Since the interest is payable in advance, a borrower of Rs. 100 actually receives only Rs. 90 and repays Rs. 100 after half a year. So the interest of Rs. 10 is earned on Rs. 90:
\( \displaystyle i = \frac{10}{90} = \frac{1}{9} \text{ per half year} \)
A year has two half years, so the effective annual rate is
\( \displaystyle r = \left(1 + \frac{1}{9}\right)^2 - 1 \)
\( \displaystyle = \frac{100}{81} - 1 = \frac{19}{81} \)
\( \approx 0.23457 \)
So the effective rate is 23.457%, given in Option (4) as 23.45% per annum.
CBSE Applied Mathematics (Class XII):
Nominal and Effective Rate of Interest
