Mathematics of FinanceMCQMTP Dec 23 Series IQuestion 1526 of 512
All Questions

Paul borrows 20,000\displaystyle 20,000 on condition to repay it with compound interest at 5%\displaystyle 5\% p.a. in annual installment of 2,000\displaystyle 2,000 each. Find the number of years in which the debt would be paid off:

Options

A10\displaystyle 10 years
B12\displaystyle 12 years
C14\displaystyle 14 years
D15\displaystyle 15 years
For any discrepancies in this question, email contact@cadada.in

Correct Answer

Option c14\displaystyle 14 years

All Options:

  • A10\displaystyle 10 years
  • B12\displaystyle 12 years
  • C14\displaystyle 14 years
  • D15\displaystyle 15 years

Ad

Detailed Solution & Explanation

The present value (PV\displaystyle PV) of the loan is: PV=A×[1(1+i)ni]PV = A \times \left[ \frac{1 - (1+i)^{-n}}{i} \right] Given: * Loan amount (PV\displaystyle PV) = 20,000\displaystyle 20,000 * Annual instalment (A\displaystyle A) = 2,000\displaystyle 2,000 * Interest rate (i\displaystyle i) = 5%\displaystyle 5\% p.a. = 0.05\displaystyle 0.05 Substituting the values: 20,000=2,000×[1(1.05)n0.05]20,000 = 2,000 \times \left[ \frac{1 - (1.05)^{-n}}{0.05} \right] 10=1(1.05)n0.0510 = \frac{1 - (1.05)^{-n}}{0.05} 0.50=1(1.05)n    (1.05)n=0.500.50 = 1 - (1.05)^{-n} \implies (1.05)^{-n} = 0.50 nln(1.05)=ln(0.50)-n \ln(1.05) = \ln(0.50) n=0.6931470.04879014.2 yearsn = \frac{0.693147}{0.048790} \approx 14.2 \text{ years} Thus, it will take approximately 14\displaystyle 14 years to pay off the debt. 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