Mathematics of FinancePYQ Jan 26Question 4258 of 507
All Questions

A sum of money lent at compound interest for 2 years at 20% p.a. would fetch ₹ 482/- more if the interest was payable half yearly then if it was payable annually. What is the value of sum deposited?

Options

A₹ 10,000
B₹ 15,000
C₹ 17,500
D₹ 20,000
For any discrepancies in this question, email contact@cadada.in

Correct Answer

Option d₹ 20,000

All Options:

  • A₹ 10,000
  • B₹ 15,000
  • C₹ 17,500
  • D₹ 20,000

Detailed Solution & Explanation

Let the sum of money deposited (principal) be P\displaystyle P. We are given: - Time t=2 years\displaystyle t = 2\text{ years} - Nominal annual interest rate r=20%\displaystyle r = 20\%
**Case 1: Interest compounded annually** The compounding frequency is once per year. A1=P(1+0.20)2=P(1.2)2=1.44PA_1 = P \left(1 + 0.20\right)^2 = P (1.2)^2 = 1.44P
**Case 2: Interest compounded half-yearly** The compounding frequency is twice per year, so the interest rate per half-year is 20%/2=10%=0.10\displaystyle 20\% / 2 = 10\% = 0.10, and the number of periods is 2×2=4\displaystyle 2 \times 2 = 4. A2=P(1+0.10)4=P(1.1)4A_2 = P \left(1 + 0.10\right)^4 = P (1.1)^4 Since (1.1)4=1.4641\displaystyle (1.1)^4 = 1.4641: A2=1.4641PA_2 = 1.4641P
The difference between the two amounts is given as ₹ 482\displaystyle \text{₹ } 482: A2A1=482A_2 - A_1 = 482 1.4641P1.44P=4821.4641P - 1.44P = 482 0.0241P=4820.0241P = 482
Solving for P\displaystyle P: P=4820.0241P = \frac{482}{0.0241} P=20,000P = 20,000 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.

Key Concepts to Understand

More Questions from Mathematics of Finance

Ready to Master Mathematics of Finance?

Practice all 507 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free