Mathematics of FinanceMCQPYQ July 21Question 1225 of 512
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A certain sum amounts to $15,748in\displaystyle in3$ years at simple interest at $1\%$ p.a. The same sum amounts to $16,510$ at r+2%\displaystyle r+2\% p.a. SI in the same time. What is the value of r\displaystyle r?

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option b — 8%\displaystyle 8\%

All Options:

  • A$10\%$
  • B8%\displaystyle 8\%
  • C$12\%$
  • D6%\displaystyle 6\%

Detailed Solution & Explanation

**Derivation of Rate of Simple Interest** Given: - Amount at r%\displaystyle r\% simple interest in 3\displaystyle 3 years (A1\displaystyle A_1) = Rs. 15,748\displaystyle Rs. \displaystyle \text{Rs. }15,748 - Amount at (r+2)%\displaystyle (r+2)\% simple interest in 3\displaystyle 3 years (A2\displaystyle A_2) = Rs. 16,510\displaystyle Rs. \displaystyle \text{Rs. }16,510 **Step 1: Express the difference in amounts** The difference in the two amounts is due to the additional simple interest earned from the increase in rate by 2%\displaystyle 2\%. Additional Simple Interest=A2−A1=16510−15748=Rs. 762\displaystyle \text{Additional Simple Interest} = A_2 - A_1 = 16510 - 15748 = \text{Rs. }762 **Step 2: Find the Principal (P\displaystyle P) using the additional simple interest** Additional SI=P×Additional Rate×t100\displaystyle \text{Additional SI} = \frac{P ×\displaystyle \times Additional Rate\displaystyle \text{Additional Rate} ×\displaystyle \times t}{100} 762=P×2×3100762 = P×2×3100\displaystyle \frac{P \times 2 \times 3}{100} 762=6P100762 = 6P100\displaystyle \frac{6P}{100} 6P=76200  ⟹  P=Rs. 12,7006P = 76200 \implies P = Rs. \displaystyle \text{Rs. }12,700 **Step 3: Solve for the rate of interest (r\displaystyle r)** Using the simple interest earned in the first case: SI1=A1−P=15748−12700=Rs. 3,048SI_1 = A_1 - P = 15748 - 12700 = Rs. \displaystyle \text{Rs. }3,048 SI1=P×r×t100SI_1 = P×r×t100\displaystyle \frac{P \times r \times t}{100} 3048=12700×r×31003048 = 12700×r×3100\displaystyle \frac{12700 \times r \times 3}{100} 3048=381r  ⟹  r=3048381=8% per annum3048 = 381 r \implies r = 3048381=8\displaystyle \frac{3048}{381} = 8\%  per annum\displaystyle \text{ per annum} 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.

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