Mathematics for FinancePYQ Nov 18Question 1188 of 512
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Rs. 8,000/−\displaystyle \text{Rs. }8,000/- at 10%\displaystyle 10\% p.a. interest compounded half yearly will become at the end of one year

Options

ARs. 8,800\displaystyle \text{Rs. }8,800
BRs. 8,820\displaystyle \text{Rs. }8,820
CRs. 8,900\displaystyle \text{Rs. }8,900
DRs. 9,000\displaystyle \text{Rs. }9,000
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Correct Answer

✅ Option b — Rs. 8,820\displaystyle \text{Rs. }8,820

All Options:

  • ARs. 8,800\displaystyle \text{Rs. }8,800
  • BRs. 8,820\displaystyle \text{Rs. }8,820
  • CRs. 8,900\displaystyle \text{Rs. }8,900
  • DRs. 9,000\displaystyle \text{Rs. }9,000

Detailed Solution & Explanation

**Derivation of Compound Interest Amount** Given: - Principal (P\displaystyle P) = Rs. 8,000\displaystyle \text{Rs. }8,000 - Nominal Rate (r\displaystyle r) = 10%\displaystyle 10\% per annum - Compounding Frequency = Half-yearly (2 times a year) - Time (t\displaystyle t) = 1\displaystyle 1 year **Step 1: Find periodic interest rate (i\displaystyle i) and total compounding periods (n\displaystyle n)** - Periodic rate i=r2=10%2=5%=0.05\displaystyle i = \frac{r}{2} = \frac{10\%}{2} = 5\% = 0.05 per half-year. - Total periods n=t×2=1×2=2\displaystyle n = t \times 2 = 1 \times 2 = 2 periods. **Step 2: Calculate the future value (A\displaystyle A)** A=P(1+i)nA = P(1 + i)^n A=8000(1+0.05)2A = 8000(1 + 0.05)^2 A=8000(1.05)2A = 8000(1.05)^2 A=8000×1.1025=Rs. 8,820A = 8000 \times 1.1025 = \text{Rs. }8,820 Hence, **Option B** is the correct answer.

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