Mathematics of FinanceMCQPYQ June 24Question 1259 of 512
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The difference between the compound interest amount and the simple interest amount for a period of two years, at same interest rate r\displaystyle r is

Options

AP×r\displaystyle P \times r
BP×r2\displaystyle P \times r^2
CP×2×r\displaystyle P \times 2 \times r
DP2×r\displaystyle P^2 \times r
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Correct Answer

✅ Option b — P×r2\displaystyle P \times r^2

All Options:

  • AP×r\displaystyle P \times r
  • BP×r2\displaystyle P \times r^2
  • CP×2×r\displaystyle P \times 2 \times r
  • DP2×r\displaystyle P^2 \times r

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Detailed Solution & Explanation

**Derivation of Difference between Compound and Simple Interest** Given: - Principal = P\displaystyle P - Interest rate = r\displaystyle r (in decimals) - Time (t\displaystyle t) = 2\displaystyle 2 years **Step 1: Write down Simple Interest (SI\displaystyle SI) and Compound Interest (CI\displaystyle CI)** - SI=P×r×2=2PrSI = P \times r \times 2 = 2Pr - CI=P(1+r)2−P=P(1+2r+r2)−P=2Pr+Pr2CI = P(1 + r)^2 - P = P(1 + 2r + r^2) - P = 2Pr + Pr^2 **Step 2: Calculate the difference** Difference=CI−SI=(2Pr+Pr2)−2Pr=Pr2\text{Difference} = CI - SI = (2Pr + Pr^2) - 2Pr = Pr^2 Thus, the difference is P×r2\displaystyle P \times r^2. 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

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Key Concepts to Understand

Compound Interest

Interest calculated on the initial principal, which also includes all of the accumulated interest of previous periods.

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More Questions from Mathematics of Finance

A sum of money invested in compounded interest doubles itself in four years. In how many years it becomes 32 times of itself as the same rate of compound interest?

The simple interest on 600\displaystyle 600 for 9 months is 27\displaystyle 27. Find the interest rate.

Miss Liza lent 4,000\displaystyle 4,000 in such a way that some amount was given to Mr. A at 3%\displaystyle 3\% p.a. S.I. and rest amount to was given to B at 5%\displaystyle 5\% p.a. S.I., the annual interest from both is 144\displaystyle 144. Find the amount lent to Mr. A.

A certain sum of money was put at S.I. for 2.5\displaystyle 2.5 years at a certain rate of S.I. p.a. Had it been put at 4%\displaystyle 4\% higher rate, it would have fetched 500\displaystyle 500 more. Find the sum of money.

Rs.1,25,000\displaystyle 1,25,000 is borrowed at compound interest at the rate of 2%\displaystyle 2\% for the 1st year, 3%\displaystyle 3\% for the second year and 4%\displaystyle 4\% for the 3rd year. Find the amount to be paid after 3 years.

If Rs. 1,000\displaystyle \text{Rs. }1,000 be invested at interest rate of 5%\displaystyle 5\% and the interest be added to the principal every 10\displaystyle 10 years, then the number in years in which it will amount to Rs. 2,000\displaystyle \text{Rs. }2,000 is:

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