Mathematics of FinanceMCQPYQ Dec 21Question 1229 of 512
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A company needs money to 10,000\displaystyle 10,000 in five years to replace as equipment. How much (in )shouldbeinvestednowataninterestrateof\displaystyle ) should be invested now at an interest rate of8\%$ p.a. is order to provide for this equipment?

Options

A6,000\displaystyle 6,000
B6,805\displaystyle 6,805
C10,000\displaystyle 10,000
D11,000\displaystyle 11,000
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Correct Answer

Option b6,805\displaystyle 6,805

All Options:

  • A6,000\displaystyle 6,000
  • B6,805\displaystyle 6,805
  • C10,000\displaystyle 10,000
  • D11,000\displaystyle 11,000

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Detailed Solution & Explanation

**Derivation of Present Value of Equipment** Given: - Future Value (A\displaystyle A) = Rs. 10,000\displaystyle \text{Rs. }10,000 - Time (t\displaystyle t) = 5\displaystyle 5 years - Rate of Interest (r\displaystyle r) = 8%\displaystyle 8\% per annum compounded annually **Step 1: Calculate the Present Value (P\displaystyle P)** A=P(1+r)tA = P(1 + r)^t 10000=P(1+0.08)510000 = P(1 + 0.08)^5 10000=P(1.08)510000 = P(1.08)^5 10000=P(1.469328)10000 = P(1.469328) P=100001.469328Rs. 6,805.83Rs. 6,805P = \frac{10000}{1.469328} \approx \text{Rs. }6,805.83 \approx \text{Rs. }6,805 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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