The effective rate of interest corresponding to a nominal rate 3% p.a payable half yearly is

Option c: 3.0225% p.a. Solution: Derivation of Effective Rate of Interest Given: - Nominal rate of interest (r) = 3% per annum - Compounding Frequency = Half-yearly (m = 2) Step 1: Calculate the periodic rate (i) i = r/m = 3%/2 = 1.5% = 0.015 text{ per half-year} Step 2: Calculate the effective annual interest rate (E) E = (1 + i)^m - 1 E = (1 + 0.015)^2 - 1 E = (1.015)^2 - 1 E = 1.030225 - 1 = 0.030225 text{ or } 3.0225% text{ p.a.} Hence, Option C is the correct answer.

The effective rate of interest corresponding to a nominal rate $3\%$ p.a payable half yearly is

The correct answer is Option c: $3.0225\%$ p.a. **Derivation of Effective Rate of Interest** Given: - Nominal rate of interest ($r$) = $3\%$ per annum - Compounding Frequency = Half-yearly ($m = 2$) **Step 1: Calculate the periodic rate ($i$)** $$i = \frac{r}{m} = \frac{3\%}{2} = 1.5\% = 0.015 \text{ per half-year}$$ **Step 2: Calculate the effective annual interest rate ($E$)** $$E = (1 + i)^m - 1$$ $$E = (1 + 0.015)^2 - 1$$ $$E = (1.015)^2 - 1$$ $$E = 1.030225 - 1 = 0.030225 \text{ or } 3.0225\% \text{ p.a.}$$ Hence, **Option C** is the correct answer.

Mathematics for FinancePYQ May 20Question 1305 of 512

All Questions

The effective rate of interest corresponding to a nominal rate $\displaystyle 3\%$ p.a payable half yearly is

Options

\displaystyle 3.2\%

p.a

\displaystyle 3.25\%

p.a

\displaystyle 3.0225\%

p.a

Dnone of these

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — $\displaystyle 3.0225\%$ p.a

All Options:

A $\displaystyle 3.2\%$ p.a
B $\displaystyle 3.25\%$ p.a
C $\displaystyle 3.0225\%$ p.a
Dnone of these

Detailed Solution & Explanation

**Derivation of Effective Rate of Interest** Given: - Nominal rate of interest (

\displaystyle r

) =

\displaystyle 3\%

per annum - Compounding Frequency = Half-yearly (

\displaystyle m = 2

) **Step 1: Calculate the periodic rate (

\displaystyle i

)**

i = \frac{r}{m} = \frac{3\%}{2} = 1.5\% = 0.015 \text{ per half-year}

**Step 2: Calculate the effective annual interest rate (

\displaystyle E

)**

E = (1 + i)^m - 1

E = (1 + 0.015)^2 - 1

E = (1.015)^2 - 1

E = 1.030225 - 1 = 0.030225 \text{ or } 3.0225\% \text{ p.a.}

Hence, **Option C** is the correct answer.

Ready to Master Mathematics for Finance?

Practice all 512 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free

The effective rate of interest corresponding to a nominal rate 3%\displaystyle 3\%3% p.a payable half yearly is