Mathematics of FinanceMCQMTP June 24 Series IIQuestion 1416 of 512
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Mr. X invests 'P' amount at Simple Interest rate 10%\displaystyle 10\% and Mr. Y invests 'Q' amount at Compound Interest rate 5%\displaystyle 5\% compounded annually. At the end of two years both get the same amount of interest, then the relation between two amounts P and Q is given by:

Options

AP=41Q80\displaystyle P = \frac{41Q}{80}
BP=41Q40\displaystyle P = \frac{41Q}{40}
CP=41Q100\displaystyle P = \frac{41Q}{100}
DP=41Q200\displaystyle P = \frac{41Q}{200}
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Correct Answer

Option aP=41Q80\displaystyle P = \frac{41Q}{80}

All Options:

  • AP=41Q80\displaystyle P = \frac{41Q}{80}
  • BP=41Q40\displaystyle P = \frac{41Q}{40}
  • CP=41Q100\displaystyle P = \frac{41Q}{100}
  • DP=41Q200\displaystyle P = \frac{41Q}{200}

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Detailed Solution & Explanation

Let IX\displaystyle I_X be the interest earned by Mr. X on principal P\displaystyle P and IY\displaystyle I_Y be the interest earned by Mr. Y on principal Q\displaystyle Q. Given parameters: * Mr. X: Rate (rX\displaystyle r_X) = 10%\displaystyle 10\% p.a. Simple Interest, Time (tX\displaystyle t_X) = 2\displaystyle 2 years IX=P×10×2100=0.20PI_X = \frac{P \times 10 \times 2}{100} = 0.20 P * Mr. Y: Rate (rY\displaystyle r_Y) = 5%\displaystyle 5\% p.a. Compound Interest, Time (tY\displaystyle t_Y) = 2\displaystyle 2 years IY=Q[(1+0.05)21]=Q[(1.05)21]=Q[1.10251]=0.1025QI_Y = Q \left[ (1 + 0.05)^2 - 1 \right] = Q [ (1.05)^2 - 1 ] = Q [ 1.1025 - 1 ] = 0.1025 Q Since both get the same amount of interest: IX=IYI_X = I_Y 0.20P=0.1025Q0.20 P = 0.1025 Q P=0.10250.20QP = \frac{0.1025}{0.20} Q P=10252000QP = \frac{1025}{2000} Q Dividing both the numerator and the denominator by 25\displaystyle 25: P=4180QP = \frac{41}{80} Q Thus, the relation between the two amounts is P=41Q80\displaystyle P = \frac{41Q}{80}. 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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