Mathematics of FinanceMCQPYQ Sep 24Question 1482 of 512
All Questions

What is the annual contribution required by an organization to accumulate 20,00,000\displaystyle 20,00,000 in ten years for the construction of a new manufacturing plant, utilizing a sinking fund with 8%\displaystyle 8\% annual interest rate of 8%\displaystyle 8\% compounded annually? (Where A(10,0.06)=13.180785\displaystyle A(10,0.06) = 13.180785)

Options

A1,67,440.90\displaystyle 1,67,440.90
B1,51,736.03\displaystyle 1,51,736.03
C1,75,433.60\displaystyle 1,75,433.60
D1,83,714.28\displaystyle 1,83,714.28
For any discrepancies in this question, email contact@cadada.in

Correct Answer

Option b1,51,736.03\displaystyle 1,51,736.03

All Options:

  • A1,67,440.90\displaystyle 1,67,440.90
  • B1,51,736.03\displaystyle 1,51,736.03
  • C1,75,433.60\displaystyle 1,75,433.60
  • D1,83,714.28\displaystyle 1,83,714.28

Ad

Detailed Solution & Explanation

The annual payment (A\displaystyle A) required for a sinking fund to accumulate a future sum FV\displaystyle FV is: A=FVFV factor=FVA(n,i)A = \frac{FV}{\text{FV factor}} = \frac{FV}{A(n, i)} Given: * Future sum (FV\displaystyle FV) = 20,00,000\displaystyle 20,00,000 * Time (n\displaystyle n) = 10\displaystyle 10 years * Using the given factor: A(10,0.06)=13.180785\displaystyle A(10, 0.06) = 13.180785 (which corresponds to 6%\displaystyle 6\% interest rate) Substituting the values: A=20,00,00013.1807851,51,736.03A = \frac{20,00,000}{13.180785} \approx 1,51,736.03 Thus, the annual contribution is approximately 1,51,736.03\displaystyle 1,51,736.03. 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.

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