The effective rate equivalent to a nominal rate of 12% compounded quarterly is: (Given \((1.03)^4=1.1256\))
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 12.56%
With 12% a year compounded quarterly, the rate per quarter is \(\frac{12\%}{4} = 3\%\), and there are 4 quarters in a year. The effective rate is the actual growth in one year:
\(r_{\text{eff}} = (1 + 0.03)^4 - 1\)
\(= 1.1256 - 1 = 0.1256\)
\(= 12.56\%\)
Why the other options are incorrect
Option (1) 14.25% — Incorrect. It does not equal \((1.03)^4 - 1 = 12.56\%\).
Option (3) 10.36% — Incorrect. It is less than the nominal 12%, but compounding more than once a year always makes the effective rate greater than the nominal rate.
Option (4) 12% — Incorrect. This is the nominal rate itself; it ignores the interest earned on interest within the year.
CBSE Applied Mathematics (Class XII):
Nominal and Effective Rate of Interest
