Mathematics of FinanceMCQPYQ July 21Question 1551 of 512
All Questions

If a person bought a house by paying 45,000.00\displaystyle 45,000.00 down payment and 80,000\displaystyle 80,000 at the end of each year till the perpetuity. Assuming the rate of interest as 16%\displaystyle 16\%, the present value of house (in $) is given as:

Options

A57,00,000\displaystyle 57,00,000
B45,00,000\displaystyle 45,00,000
C50,00,000\displaystyle 50,00,000
D5,00,000\displaystyle 5,00,000
For any discrepancies in this question, email contact@cadada.in

Correct Answer

Option b45,00,000\displaystyle 45,00,000

All Options:

  • A57,00,000\displaystyle 57,00,000
  • B45,00,000\displaystyle 45,00,000
  • C50,00,000\displaystyle 50,00,000
  • D5,00,000\displaystyle 5,00,000

Ad

Detailed Solution & Explanation

The present value (PV\displaystyle PV) of the house is the down payment plus the present value of the perpetuity: PV=Down Payment+AiPV = \text{Down Payment} + \frac{A}{i} Given: * Down Payment = 45,000\displaystyle 45,000 * Perpetual annual payment (A\displaystyle A) = 80,000\displaystyle 80,000 * Interest rate (i\displaystyle i) = 16%\displaystyle 16\% p.a. = 0.16\displaystyle 0.16 Substituting the values: PV=45,000+80,0000.16=45,000+5,00,000=5,45,000PV = 45,000 + \frac{80,000}{0.16} = 45,000 + 5,00,000 = 5,45,000 Mathematically, the present value is 5,45,000\displaystyle 5,45,000. However, the official key marks Option B (45,00,000\displaystyle 45,00,000). 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

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.

Related Comparison Tables

More Questions from Mathematics of Finance

Ready to Master Mathematics of Finance?

Practice all 512 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free