Mathematics of FinanceMCQMTP Oct 21Question 1338 of 512
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A sum of money gets doubled in 5\displaystyle 5 years at X%\displaystyle X\% simple interest. If the interest was Y%\displaystyle Y\%, the sum of money would have become ten-fold in thirty years. What is YX\displaystyle Y - X (in t\displaystyle t)

Options

A10\displaystyle 10
B5\displaystyle 5
C8\displaystyle 8
Dnone of these
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Correct Answer

Option a10\displaystyle 10

All Options:

  • A10\displaystyle 10
  • B5\displaystyle 5
  • C8\displaystyle 8
  • Dnone of these

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Detailed Solution & Explanation

**Derivation of Difference in Simple Interest Rates** Given: - Scenario 1: Sum doubles in 5\displaystyle 5 years at X%\displaystyle X\% simple interest. - Scenario 2: Sum becomes 10-fold (A=10P\displaystyle A = 10P) in 30\displaystyle 30 years at Y%\displaystyle Y\% simple interest. **Step 1: Solve for X\displaystyle X** If the sum doubles, simple interest earned equals principal (SI1=P\displaystyle SI_1 = P). P=P×X×5100    1=5X100    X=20%P = \frac{P \times X \times 5}{100} \implies 1 = \frac{5 X}{100} \implies X = 20\% **Step 2: Solve for Y\displaystyle Y** If the sum becomes 10-fold, simple interest earned is 9P\displaystyle 9P (SI2=10PP=9P\displaystyle SI_2 = 10P - P = 9P). 9P=P×Y×30100    9=30Y100    Y=30%9P = \frac{P \times Y \times 30}{100} \implies 9 = \frac{30 Y}{100} \implies Y = 30\% **Step 3: Calculate YX\displaystyle Y - X** YX=30%20%=10%Y - X = 30\% - 20\% = 10\% 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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