Mathematics for FinancePYQ Dec 23Question 1255 of 512
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Compute the compound interest on 6,000\displaystyle 6,000 for 1.25\displaystyle 1.25 years at 8%\displaystyle 8\% per annum. Interest will be compounded quarterly

Options

A642\displaystyle 642
B630.78\displaystyle 630.78
C634.68\displaystyle 634.68
D624.48\displaystyle 624.48
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Correct Answer

✅ Option d — 624.48\displaystyle 624.48

All Options:

  • A642\displaystyle 642
  • B630.78\displaystyle 630.78
  • C634.68\displaystyle 634.68
  • D624.48\displaystyle 624.48

Detailed Solution & Explanation

**Derivation of Compound Interest** Given: - Principal (P\displaystyle P) = Rs. 6,000\displaystyle \text{Rs. }6,000 - Rate of Interest (r\displaystyle r) = 8%\displaystyle 8\% per annum compounded quarterly - Time (t\displaystyle t) = 1.25\displaystyle 1.25 years **Step 1: Calculate periodic rate (i\displaystyle i) and number of periods (n\displaystyle n)** - Periodic rate i=r4=8%4=2%=0.02\displaystyle i = \frac{r}{4} = \frac{8\%}{4} = 2\% = 0.02 per quarter. - Number of periods n=t×4=1.25×4=5\displaystyle n = t \times 4 = 1.25 \times 4 = 5 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=6000(1+0.02)5A = 6000(1 + 0.02)^5 A=6000(1.02)5A = 6000(1.02)^5 A≈6000×1.104081=Rs. 6,624.48A \approx 6000 \times 1.104081 = \text{Rs. }6,624.48 CI=A−P=6624.48−6000=Rs. 624.48CI = A - P = 6624.48 - 6000 = \text{Rs. }624.48 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

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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.

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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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