Mathematics of FinanceMCQPYQ June 22Question 1544 of 512
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ABC Ltd. Wants to lease out an asset costing 3,60,000\displaystyle 3,60,000 for a five year period. It has a fixed rental of 1,05,000\displaystyle 1,05,000, per annum payable annually starting from the end of first year. Suppose rate of interest is 14%\displaystyle 14\% per annum compounded annually on which money can be invested by the company. Is this agreement favourable to the company.

Options

AYes
BNo
CIt depends
DNone of these
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Correct Answer

Option aYes

All Options:

  • AYes
  • BNo
  • CIt depends
  • DNone of these

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Detailed Solution & Explanation

To determine whether the lease agreement is favorable, we calculate the Present Value (PV\displaystyle PV) of the lease rentals and compare it with the asset cost: PV=R×[1(1+i)ni]PV = R \times \left[ \frac{1 - (1+i)^{-n}}{i} \right] Given: * Annual lease rental (R\displaystyle R) = 1,05,000\displaystyle 1,05,000 * Time (n\displaystyle n) = 5\displaystyle 5 years * Interest rate (i\displaystyle i) = 14%\displaystyle 14\% p.a. = 0.14\displaystyle 0.14 Substituting the values: PV=1,05,000×[1(1.14)50.14]PV = 1,05,000 \times \left[ \frac{1 - (1.14)^{-5}}{0.14} \right] Using (1.14)50.51937\displaystyle (1.14)^{-5} \approx 0.51937: PV=1,05,000×3.433083,60,473.50PV = 1,05,000 \times 3.43308 \approx 3,60,473.50 Since the Present Value of the lease rentals (3,60,473.50\displaystyle 3,60,473.50) is greater than the cost of the asset (3,60,000\displaystyle 3,60,000), the leasing agreement is favorable to the lessor. Hence, **Option A** 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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