Mathematics for FinancePYQ Sep 24Question 1267 of 512
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The compound interest on 40,000\displaystyle 40,000 at 12%\displaystyle 12\% per annum compounded quarterly for 6\displaystyle 6 months is:

Options

A2,463\displaystyle 2,463
B2,643\displaystyle 2,643
C2,364\displaystyle 2,364
D2,436\displaystyle 2,436
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Correct Answer

✅ Option d — 2,436\displaystyle 2,436

All Options:

  • A2,463\displaystyle 2,463
  • B2,643\displaystyle 2,643
  • C2,364\displaystyle 2,364
  • D2,436\displaystyle 2,436

Detailed Solution & Explanation

**Derivation of Compound Interest** Given: - Principal (P\displaystyle P) = Rs. 40,000\displaystyle \text{Rs. }40,000 - Nominal Rate (r\displaystyle r) = 12%\displaystyle 12\% per annum compounded quarterly - Time (t\displaystyle t) = 6\displaystyle 6 months = 0.5\displaystyle 0.5 years **Step 1: Find periodic rate (i\displaystyle i) and compounding periods (n\displaystyle n)** - Periodic rate i=r4=12%4=3%=0.03\displaystyle i = \frac{r}{4} = \frac{12\%}{4} = 3\% = 0.03 per quarter. - Number of quarters n=t×4=0.5×4=2\displaystyle n = t \times 4 = 0.5 \times 4 = 2 quarters. **Step 2: Calculate Future Value (A\displaystyle A) and Compound Interest (CI\displaystyle CI)** A=P(1+i)nA = P(1 + i)^n A=40000(1+0.03)2A = 40000(1 + 0.03)^2 A=40000(1.0609)=Rs. 42,436A = 40000(1.0609) = \text{Rs. }42,436 CI=A−P=42436−40000=Rs. 2,436CI = A - P = 42436 - 40000 = \text{Rs. }2,436 Hence, **Option D** is the correct answer.

Key Concepts to Understand

Compound Interest

Interest calculated on the initial principal, which also includes all of the accumulated interest of previous periods.

More Questions from Mathematics for Finance

A sum of money invested in compounded interest doubles itself in four years. In how many years it becomes 32 times of itself as the same rate of compound interest?

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A certain sum of money was put at S.I. for 2.5\displaystyle 2.5 years at a certain rate of S.I. p.a. Had it been put at 4%\displaystyle 4\% higher rate, it would have fetched 500\displaystyle 500 more. Find the sum of money.

Rs.1,25,000\displaystyle 1,25,000 is borrowed at compound interest at the rate of 2%\displaystyle 2\% for the 1st year, 3%\displaystyle 3\% for the second year and 4%\displaystyle 4\% for the 3rd year. Find the amount to be paid after 3 years.

If Rs. 1,000\displaystyle \text{Rs. }1,000 be invested at interest rate of 5%\displaystyle 5\% and the interest be added to the principal every 10\displaystyle 10 years, then the number in years in which it will amount to Rs. 2,000\displaystyle \text{Rs. }2,000 is:

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