Mathematics of FinanceMCQMTP Oct 21Question 1341 of 512
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The compound interest earned by a money lender on 7,000\displaystyle 7,000 for 3\displaystyle 3 years at the rate of interest for 3\displaystyle 3 years are 7%\displaystyle 7\%, 8%\displaystyle 8\% and 8.5%\displaystyle 8.5\% is

Options

A1750\displaystyle 1750
B1800\displaystyle 1800
C1776\displaystyle 1776
Dnone of these
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Correct Answer

Option c1776\displaystyle 1776

All Options:

  • A1750\displaystyle 1750
  • B1800\displaystyle 1800
  • C1776\displaystyle 1776
  • Dnone of these

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Detailed Solution & Explanation

**Derivation of Compound Interest with Varying Rates** Given: - Principal (P\displaystyle P) = Rs. 7,000\displaystyle \text{Rs. }7,000 - Time (t\displaystyle t) = 3\displaystyle 3 years - Rates for successive years: r1=7%\displaystyle r_1 = 7\%, r2=8%\displaystyle r_2 = 8\%, r3=8.5%\displaystyle r_3 = 8.5\% **Step 1: Calculate the future value (A\displaystyle A)** A=P(1+r1)(1+r2)(1+r3)A = P(1 + r_1)(1 + r_2)(1 + r_3) A=7000(1+0.07)(1+0.08)(1+0.085)A = 7000(1 + 0.07)(1 + 0.08)(1 + 0.085) A=7000(1.07)(1.08)(1.085)A = 7000(1.07)(1.08)(1.085) **Step 2: Compute the product** 1.07×1.08×1.085=1.2538141.07 \times 1.08 \times 1.085 = 1.253814 A=7000×1.253814=Rs. 8,776.70A = 7000 \times 1.253814 = \text{Rs. }8,776.70 **Step 3: Calculate Compound Interest (CI\displaystyle CI)** CI=AP=8776.707000=Rs. 1,776.70Rs. 1,776CI = A - P = 8776.70 - 7000 = \text{Rs. }1,776.70 \approx \text{Rs. }1,776 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

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