Mathematics of FinanceMCQMTP June 22Question 1356 of 512
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The rate of interest for the first 2\displaystyle 2 year is 3%\displaystyle 3\% per annum, for next 3\displaystyle 3 years is 8%\displaystyle 8\% per annum and for the period beyond 5\displaystyle 5 years, 10%\displaystyle 10\% per annum. If a man gets 1520\displaystyle 1520 as a simple interest for 6\displaystyle 6 years, how much money did he deposit?

Options

A3800\displaystyle 3800
B3000\displaystyle 3000
C4000\displaystyle 4000
DNone of these
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Correct Answer

Option a3800\displaystyle 3800

All Options:

  • A3800\displaystyle 3800
  • B3000\displaystyle 3000
  • C4000\displaystyle 4000
  • DNone of these

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Detailed Solution & Explanation

**Derivation of Principal Sum** Given: - Total Simple Interest received (SI\displaystyle SI) = Rs. 1,520\displaystyle \text{Rs. }1,520 for t=6\displaystyle t = 6 years - Rate structure: - For first 2\displaystyle 2 years: r1=3%\displaystyle r_1 = 3\% per annum - For next 3\displaystyle 3 years: r2=8%\displaystyle r_2 = 8\% per annum - For the period beyond 5\displaystyle 5 years (which is 1\displaystyle 1 year in this case): r3=10%\displaystyle r_3 = 10\% per annum **Step 1: Calculate the total cumulative interest percentage** Total R×T=(2×3%)+(3×8%)+(1×10%)=6%+24%+10%=40%\text{Total } R \times T = (2 \times 3\%) + (3 \times 8\%) + (1 \times 10\%)= 6\% + 24\% + 10\% = 40\% **Step 2: Set up simple interest formula and solve for Principal (P\displaystyle P)** SI=P×Total R×T100SI = P \times \frac{\text{Total } R \times T}{100} 1520=P×0.401520 = P \times 0.40 P=15200.40=Rs. 3,800P = \frac{1520}{0.40} = \text{Rs. }3,800 *(Note: The database lists Option B (3,000\displaystyle 3,000) as correct, which is mathematically incorrect. The correct principal is 3,800, which is Option A.)* 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

Exam Strategy Tip

Guaranteed 12-16 marks. Master your calculator! Learn the 'GT' and compound interest M+/M- tricks to solve annuity questions in 10 seconds without writing long formulas.

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