Mathematics for FinancePYQ 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 b — 6,805\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

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=100001.469328≈Rs. 6,805.83≈Rs. 6,805P = \frac{10000}{1.469328} \approx \text{Rs. }6,805.83 \approx \text{Rs. }6,805 Hence, **Option B** is the correct answer.

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