Mathematics for FinanceMTP June 22Question 1353 of 512
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Find the effective rate of interest if an amount of 30,000\displaystyle 30,000 deposited in a bank. For 1\displaystyle 1 year at the rate of 10%\displaystyle 10\% p.a. compounded semi-annually.

Options

A10.05%\displaystyle 10.05\%
B10.10%\displaystyle 10.10\%
C10.20%\displaystyle 10.20\%
D10.25%\displaystyle 10.25\%
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Correct Answer

✅ Option d — 10.25%\displaystyle 10.25\%

All Options:

  • A10.05%\displaystyle 10.05\%
  • B10.10%\displaystyle 10.10\%
  • C10.20%\displaystyle 10.20\%
  • D10.25%\displaystyle 10.25\%

Detailed Solution & Explanation

**Derivation of Effective Rate of Interest** Given: - Nominal interest rate (r\displaystyle r) = 10%\displaystyle 10\% per annum compounded semi-annually **Step 1: Calculate periodic rate (i\displaystyle i) and number of periods (m\displaystyle m)** - Periodic rate i=10%2=5%=0.05\displaystyle i = \frac{10\%}{2} = 5\% = 0.05 per half-year. - Compounding periods per year m=2\displaystyle m = 2. **Step 2: Calculate the effective annual interest rate (E\displaystyle E)** E=(1+i)m−1E = (1 + i)^m - 1 E=(1+0.05)2−1E = (1 + 0.05)^2 - 1 E=(1.05)2−1E = (1.05)^2 - 1 E=1.1025−1=0.1025 or 10.25%E = 1.1025 - 1 = 0.1025 \text{ or } 10.25\% *(Note: The database lists Option A (10.05%\displaystyle 10.05\%) as correct, which is a typo in the key. The mathematically correct rate is 10.25%, which is Option D.)* Hence, **Option D** is the correct answer.

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