Mathematics of FinanceMCQMTP Dec 23 Series IIQuestion 3953 of 512
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A certain sum of money was put at S.I. for 2.5\displaystyle 2.5 years at a certain rate of S.I. p.a. Had it been put at 4%\displaystyle 4\% higher rate, it would have fetched 500\displaystyle 500 more. Find the sum of money.

Options

A4,000\displaystyle 4,000
B5,000\displaystyle 5,000
C6,000\displaystyle 6,000
DNone of these
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Correct Answer

Option b5,000\displaystyle 5,000

All Options:

  • A4,000\displaystyle 4,000
  • B5,000\displaystyle 5,000
  • C6,000\displaystyle 6,000
  • DNone of these

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Detailed Solution & Explanation

Let the principal amount (sum of money) be P\displaystyle P. Let the initial rate of simple interest be r%\displaystyle r\% p.a. The interest earned in 2.5\displaystyle 2.5 years is: SI1=P×r×2.5100SI_1 = \frac{P \times r \times 2.5}{100} If the interest rate were 4%\displaystyle 4\% higher, the new rate would be (r+4)%\displaystyle (r + 4)\% p.a., and the interest earned would be: SI2=P×(r+4)×2.5100SI_2 = \frac{P \times (r + 4) \times 2.5}{100} The difference in simple interest is given as Rs. 500\displaystyle \text{Rs. }500: SI2SI1=500SI_2 - SI_1 = 500 P×(r+4)×2.5100P×r×2.5100=500\frac{P \times (r + 4) \times 2.5}{100} - \frac{P \times r \times 2.5}{100} = 500 P×2.5100×(r+4r)=500\frac{P \times 2.5}{100} \times (r + 4 - r) = 500 P×0.025×4=500P \times 0.025 \times 4 = 500 0.1P=5000.1P = 500 Solving for P\displaystyle P: P=5000.1=5,000P = \frac{500}{0.1} = 5,000 Thus, the sum of money is Rs. 5,000\displaystyle \text{Rs. }5,000. Hence, **Option B** 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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