Mathematics of FinanceMCQMTP May 20, ICAI SMQuestion 1507 of 512
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A person bought a house paying $20,000$ cash down and $4,000$ at the end of each year for $25yrs.at\displaystyle yrs. at5\%$ p.a. C.I. The cash down price is

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option d — None of these

All Options:

  • A$75,000$
  • B$76,900$
  • C$76,375.80$
  • DNone of these

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\displaystyle \text{Cash Down Price} = \text{Down Payment} + PV_{annuity\displaystyle \text{annuity}} Given: * Down payment = $20,000$ * Annual payment (A\displaystyle A) = $4,000$ * Time (n\displaystyle n) = $25$ years * Interest rate (i\displaystyle i) = 5%\displaystyle 5\% p.a. = $0.05$ The present value of the annuity is: PVannuity=4,000×[1−(1.05)−250.05]PV_{annuity\displaystyle \text{annuity}} = 4,000 ×\displaystyle \times \left[ 1−(1.05)−250.05\displaystyle \frac{1 - (1.05)^{-25}}{0.05} \right] Using (1.05)25≈3.386355\displaystyle (1.05)^{25} ≈\displaystyle \approx 3.386355: PVannuity=4,000×14.09394≈56,375.78PV_{annuity\displaystyle \text{annuity}} = 4,000 ×\displaystyle \times 14.09394 ≈\displaystyle \approx 56,375.78 Thus, the cash down price is: Cash Down Price=20,000+56,375.78=76,375.78Cash Down Price=20\displaystyle \text{Cash Down Price} = 20,000 + 56,375.78 = 76,375.78 While Option C ($76,375.80$) 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

Guaranteed 12-16 marks. Master your calculator! Learn the 'GT' and compound interest M+/M- tricks to solve annuity questions in 10 seconds without writing long formulas.

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