Mathematics of FinanceMCQMTP Sep 24 Series IIQuestion 1432 of 512
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The Partners A & B together lent $3903at\displaystyle at4\%$ p.a interest compounded annually. After a span of $7$ years A gets the same amount as B gets after $9$ years. The share of A is sum of $3903$ would have been

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option c — $2028$

All Options:

  • A$1875$
  • B$2280$
  • C$2028$
  • D$2820$

Detailed Solution & Explanation

Let the share of partner A be x\displaystyle x. Since the total amount lent is Rs. 3,903\displaystyle Rs. \displaystyle \text{Rs. }3,903, the share of partner B is $3,903 - x$. Given parameters: * Rate of interest (r\displaystyle r) = 4%\displaystyle 4\% p.a. compounded annually, so i=0.04\displaystyle i = 0.04 * A's investment period = 7\displaystyle 7 years * B's investment period = 9\displaystyle 9 years According to the question, the amount A gets after 7\displaystyle 7 years is equal to the amount B gets after 9\displaystyle 9 years: x(1+i)7=(3,903−x)(1+i)9x(1+i)^7 = (3,903 - x)(1+i)^9 Dividing both sides by (1+i)7\displaystyle (1+i)^7: x=(3,903−x)(1+i)2x = (3,903 - x)(1+i)^2 x=(3,903−x)(1.04)2x = (3,903 - x)(1.04)^2 x=(3,903−x)(1.0816)x = (3,903 - x)(1.0816) x=4221.4848−1.0816xx = 4221.4848 - 1.0816x 2.0816x=4221.48482.0816x = 4221.4848 Solving for x\displaystyle x: x=4221.48482.0816=2,028x = 4221.48482.0816=2\displaystyle \frac{4221.4848}{2.0816} = 2,028 Thus, the share of A in the sum of $3,903is\displaystyle isRs. \displaystyle \text{Rs. }2,028$. Hence, **Option C** 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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