Mathematics of FinanceMCQMTP Dec 22 Series IIQuestion 1375 of 512
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Mr. X lent some amount of money at 4%\displaystyle 4\% S.I. and he obtained 520\displaystyle 520 less than he lent in 5\displaystyle 5 years. The sum lent is

Options

A650\displaystyle 650
B750\displaystyle 750
C620\displaystyle 620
Dnone of these
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Correct Answer

Option a650\displaystyle 650

All Options:

  • A650\displaystyle 650
  • B750\displaystyle 750
  • C620\displaystyle 620
  • Dnone of these

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Detailed Solution & Explanation

**Derivation of Sum Lent** Given: - Rate of simple interest (R\displaystyle R) = 4%\displaystyle 4\% per annum - Time (T\displaystyle T) = 5\displaystyle 5 years - Interest obtained is Rs. 520\displaystyle \text{Rs. }520 less than the principal (SI=P520\displaystyle SI = P - 520) **Step 1: Set up the Simple Interest equation** SI=P×R×T100SI = \frac{P \times R \times T}{100} P520=P×4×5100P - 520 = \frac{P \times 4 \times 5}{100} P520=0.20PP - 520 = 0.20 P **Step 2: Solve for P\displaystyle P** P0.20P=520P - 0.20 P = 520 0.80P=5200.80 P = 520 P=5200.80=Rs. 650P = \frac{520}{0.80} = \text{Rs. }650 *(Note: The database lists Option B (750\displaystyle 750) as correct, which is a typo in the key. The mathematically correct sum lent is 650, which is Option A.)* Hence, **Option A** 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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