Mathematics of FinanceMCQMTP Jun 23 Series IIQuestion 3940 of 512
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1,25,000\displaystyle 1,25,000 is borrowed at compound interest at the rate of 2%\displaystyle 2\% for the 1\displaystyle 1st year, 3%\displaystyle 3\% for the 2\displaystyle 2nd year and 4%\displaystyle 4\% for the 3\displaystyle 3rd year. Find the amount to be paid after 3\displaystyle 3 years

Options

A125678\displaystyle 125678
B136587\displaystyle 136587
C163378\displaystyle 163378
D136578\displaystyle 136578
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Correct Answer

Option d136578\displaystyle 136578

All Options:

  • A125678\displaystyle 125678
  • B136587\displaystyle 136587
  • C163378\displaystyle 163378
  • D136578\displaystyle 136578

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Detailed Solution & Explanation

To find the amount to be paid after 3\displaystyle 3 years, we use the formula for compound interest with successive interest rates: A=P(1+r1100)(1+r2100)(1+r3100)A = P \left(1 + \frac{r_1}{100}\right) \left(1 + \frac{r_2}{100}\right) \left(1 + \frac{r_3}{100}\right) Given parameters: * Principal (P\displaystyle P) = Rs. 1,25,000\displaystyle \text{Rs. }1,25,000 * Rate for the 1st year (r1\displaystyle r_1) = 2%\displaystyle 2\% p.a. * Rate for the 2nd year (r2\displaystyle r_2) = 3%\displaystyle 3\% p.a. * Rate for the 3rd year (r3\displaystyle r_3) = 4%\displaystyle 4\% p.a. Substituting the values into the formula: A=1,25,000×(1+2100)×(1+3100)×(1+4100)A = 1,25,000 \times \left(1 + \frac{2}{100}\right) \times \left(1 + \frac{3}{100}\right) \times \left(1 + \frac{4}{100}\right) A=1,25,000×1.02×1.03×1.04A = 1,25,000 \times 1.02 \times 1.03 \times 1.04 Let's calculate step-by-step: 1,25,000×1.02=1,27,5001,25,000 \times 1.02 = 1,27,500 1,27,500×1.03=1,31,3251,27,500 \times 1.03 = 1,31,325 1,31,325×1.04=1,36,5781,31,325 \times 1.04 = 1,36,578 Thus, the amount to be paid after 3\displaystyle 3 years is Rs. 1,36,578\displaystyle \text{Rs. }1,36,578. Hence, **Option D** 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.

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