Mathematics of FinanceMCQPYQ July 21Question 1224 of 512
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A sum of 7,500\displaystyle 7,500 amounts to 9,075\displaystyle 9,075 at 10%\displaystyle 10\% p.a., interest being compounded yearly in a certain time. The simple interest on the same sum for the same time and the same rate is:

Options

A1,000\displaystyle 1,000
B1,250\displaystyle 1,250
C1,800\displaystyle 1,800
D1,500\displaystyle 1,500
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Correct Answer

✅ Option d — 1,500\displaystyle 1,500

All Options:

  • A1,000\displaystyle 1,000
  • B1,250\displaystyle 1,250
  • C1,800\displaystyle 1,800
  • D1,500\displaystyle 1,500

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Detailed Solution & Explanation

**Derivation of Simple Interest from Compound Interest** Given: - Principal (P\displaystyle P) = Rs. 7,500\displaystyle \text{Rs. }7,500 - Amount (A\displaystyle A) = Rs. 9,075\displaystyle \text{Rs. }9,075 - Rate of Interest (R\displaystyle R) = 10%\displaystyle 10\% per annum compounded annually **Step 1: Determine the time period (t\displaystyle t)** A=P(1+R100)tA = P\left(1 + \frac{R}{100}\right)^t 9075=7500(1+0.10)t9075 = 7500(1 + 0.10)^t 90757500=(1.1)t\frac{9075}{7500} = (1.1)^t 1.21=(1.1)t  ⟹  (1.1)2=(1.1)t  ⟹  t=2 years1.21 = (1.1)^t \implies (1.1)^2 = (1.1)^t \implies t = 2 \text{ years} **Step 2: Calculate Simple Interest (SI\displaystyle SI) for the same Principal, Rate, and Time** SI=P×R×t100SI = \frac{P \times R \times t}{100} SI=7500×10×2100=Rs. 1,500SI = \frac{7500 \times 10 \times 2}{100} = \text{Rs. }1,500 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

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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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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.

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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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