Mathematics of FinanceMCQMTP Sep 24 Series IIQuestion 1426 of 512
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The simple interest on a certain sum of money is 125\displaystyle \frac{1}{25} times of principal, the rate of interest when rate of interest and time are equal is

Options

A2%\displaystyle 2\%
B3%\displaystyle 3\%
C4%\displaystyle 4\%
DNone of these
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Correct Answer

Option a2%\displaystyle 2\%

All Options:

  • A2%\displaystyle 2\%
  • B3%\displaystyle 3\%
  • C4%\displaystyle 4\%
  • DNone of these

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Detailed Solution & Explanation

Let the principal amount be P\displaystyle P. We are given that the Simple Interest (SI\displaystyle SI) on the sum is 125\displaystyle \frac{1}{25} times the principal: SI=125PSI = \frac{1}{25} P Let the rate of interest be r%\displaystyle r\% p.a. and the time period be t\displaystyle t years. We are given that the rate of interest and time are equal: t=rt = r The formula for Simple Interest is: SI=P×r×t100SI = \frac{P \times r \times t}{100} Substituting the values into the formula: 125P=P×r×r100\frac{1}{25} P = \frac{P \times r \times r}{100} 125=r2100\frac{1}{25} = \frac{r^2}{100} r2=10025=4r^2 = \frac{100}{25} = 4 Taking the square root on both sides: r=2r = 2 Thus, the rate of interest is 2%\displaystyle 2\%. 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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