Mathematics of FinanceMCQMTP May 20, ICAI SMQuestion 1507 of 512
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A person bought a house paying 20,000\displaystyle 20,000 cash down and 4,000\displaystyle 4,000 at the end of each year for 25\displaystyle 25 yrs. at 5%\displaystyle 5\% p.a. C.I. The cash down price is

Options

A75,000\displaystyle 75,000
B76,900\displaystyle 76,900
C76,375.80\displaystyle 76,375.80
DNone of these
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Correct Answer

Option dNone of these

All Options:

  • A75,000\displaystyle 75,000
  • B76,900\displaystyle 76,900
  • C76,375.80\displaystyle 76,375.80
  • DNone of these

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Detailed Solution & Explanation

The cash down price of the house is the down payment plus the present value of the annual payments: Cash Down Price=Down Payment+PVannuity\text{Cash Down Price} = \text{Down Payment} + PV_{\text{annuity}} Given: * Down payment = 20,000\displaystyle 20,000 * Annual payment (A\displaystyle A) = 4,000\displaystyle 4,000 * Time (n\displaystyle n) = 25\displaystyle 25 years * Interest rate (i\displaystyle i) = 5%\displaystyle 5\% p.a. = 0.05\displaystyle 0.05 The present value of the annuity is: PVannuity=4,000×[1(1.05)250.05]PV_{\text{annuity}} = 4,000 \times \left[ \frac{1 - (1.05)^{-25}}{0.05} \right] Using (1.05)253.386355\displaystyle (1.05)^{25} \approx 3.386355: PVannuity=4,000×14.0939456,375.78PV_{\text{annuity}} = 4,000 \times 14.09394 \approx 56,375.78 Thus, the cash down price is: Cash Down Price=20,000+56,375.78=76,375.78\text{Cash Down Price} = 20,000 + 56,375.78 = 76,375.78 While Option C (76,375.80\displaystyle 76,375.80) is mathematically closest, the official key marks Option D (None of these). Hence, **Option D** 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

Exam Strategy Tip

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