Mathematics of FinanceMCQPYQ Dec 22Question 1239 of 512
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Mr. Prakash invested money in two schemes 'A' and 'B' offering compound interest at the rate of 8%\displaystyle 8\% and 9%\displaystyle 9\% p.a. respectively. If the total amount of interest accrued through these two schemes together in two years was 4,816.30\displaystyle 4,816.30 and total amount invested was 27,000\displaystyle 27,000. What was the amount invested in schemes 'A'?

Options

A12,000\displaystyle 12,000
B12,500\displaystyle 12,500
C13,000\displaystyle 13,000
D13,500\displaystyle 13,500
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Correct Answer

Option a12,000\displaystyle 12,000

All Options:

  • A12,000\displaystyle 12,000
  • B12,500\displaystyle 12,500
  • C13,000\displaystyle 13,000
  • D13,500\displaystyle 13,500

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Detailed Solution & Explanation

**Derivation of Invested Sum in Scheme A** *Note: The question contains a small typo in the total interest accrued, stating it is 4,816.30. In standard CA Foundation problems, this interest is 4,818.30, which leads to an integer solution of 12,000.* Given: - Total investment = Rs. 27,000\displaystyle \text{Rs. }27,000 - Scheme A rate (r1\displaystyle r_1) = 8%\displaystyle 8\% compounded annually - Scheme B rate (r2\displaystyle r_2) = 9%\displaystyle 9\% compounded annually - Time (t\displaystyle t) = 2\displaystyle 2 years - Let the investment in Scheme A be x\displaystyle x. - Then, investment in Scheme B is (27,000x)\displaystyle (27,000 - x). **Step 1: Write down the interest from each scheme** - Scheme A Interest: CIA=x[(1.08)21]=0.1664xCI_A = x \left[(1.08)^2 - 1\right] = 0.1664 x - Scheme B Interest: CIB=(27000x)[(1.09)21]=(27000x)×0.1881=5078.700.1881xCI_B = (27000 - x) \left[(1.09)^2 - 1\right] = (27000 - x) \times 0.1881 = 5078.70 - 0.1881 x **Step 2: Set up the total interest equation** 0.1664x+5078.700.1881x=4818.300.1664 x + 5078.70 - 0.1881 x = 4818.30 0.0217x=4818.305078.70-0.0217 x = 4818.30 - 5078.70 0.0217x=260.40-0.0217 x = -260.40 x=260.400.0217=Rs. 12,000x = \frac{260.40}{0.0217} = \text{Rs. }12,000 *(Using the database value of 4,816.30 yields x=12,092.17\displaystyle x = 12,092.17, which is closest to Option A/B).* Hence, **Option A** is the correct answer.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

Weightage

12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

View Official ICAI Syllabus

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