Mathematics of FinanceMCQMTP May 20Question 1510 of 512
All Questions

The present value of 10,000\displaystyle 10,000 due in 2\displaystyle 2 years at 5%\displaystyle 5\% p.a. compound interest when the interest is paid on half-yearly basis is

Options

A9,070\displaystyle 9,070
B9,070\displaystyle 9,070
C9,060\displaystyle 9,060
Dnone of these
For any discrepancies in this question, email contact@cadada.in

Correct Answer

Option c9,060\displaystyle 9,060

All Options:

  • A9,070\displaystyle 9,070
  • B9,070\displaystyle 9,070
  • C9,060\displaystyle 9,060
  • Dnone of these

Ad

Detailed Solution & Explanation

The present value (PV\displaystyle PV) of a future sum compounded semi-annually is: PV=FV(1+r2)2nPV = \frac{FV}{\left(1 + \frac{r}{2}\right)^{2n}} Given: * Future Value (FV\displaystyle FV) = 10,000\displaystyle 10,000 * Time (n\displaystyle n) = 2\displaystyle 2 years * Nominal rate (r\displaystyle r) = 5%\displaystyle 5\% p.a. = 0.05\displaystyle 0.05 Substituting the values: PV=10,000(1+0.025)4=10,000(1.025)4=10,0001.1038139,059.509,060PV = \frac{10,000}{(1 + 0.025)^4} = \frac{10,000}{(1.025)^4} = \frac{10,000}{1.103813} \approx 9,059.50 \approx 9,060 Hence, **Option C** 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.

Key Concepts to Understand

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