Mathematics of FinanceMCQMTP Sep 24 Series IIQuestion 1432 of 512
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The Partners A & B together lent 3903\displaystyle 3903 at 4%\displaystyle 4\% p.a interest compounded annually. After a span of 7\displaystyle 7 years A gets the same amount as B gets after 9\displaystyle 9 years. The share of A is sum of 3903\displaystyle 3903 would have been

Options

A1875\displaystyle 1875
B2280\displaystyle 2280
C2028\displaystyle 2028
D2820\displaystyle 2820
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Correct Answer

Option c2028\displaystyle 2028

All Options:

  • A1875\displaystyle 1875
  • B2280\displaystyle 2280
  • C2028\displaystyle 2028
  • D2820\displaystyle 2820

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Detailed Solution & Explanation

Let the share of partner A be x\displaystyle x. Since the total amount lent is Rs. 3,903\displaystyle \text{Rs. }3,903, the share of partner B is 3,903x\displaystyle 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=(3,903x)(1+i)9x(1+i)^7 = (3,903 - x)(1+i)^9 Dividing both sides by (1+i)7\displaystyle (1+i)^7: x=(3,903x)(1+i)2x = (3,903 - x)(1+i)^2 x=(3,903x)(1.04)2x = (3,903 - x)(1.04)^2 x=(3,903x)(1.0816)x = (3,903 - x)(1.0816) x=4221.48481.0816xx = 4221.4848 - 1.0816x 2.0816x=4221.48482.0816x = 4221.4848 Solving for x\displaystyle x: x=4221.48482.0816=2,028x = \frac{4221.4848}{2.0816} = 2,028 Thus, the share of A in the sum of 3,903\displaystyle 3,903 is Rs. 2,028\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.

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