Mathematics of FinanceMCQPYQ Dec 23Question 1469 of 512
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Suppose Mr. X invested 5,000\displaystyle 5,000 every year starting from today in mutual fund for next 10\displaystyle 10 years. Assuming that interest compounded annually is at 18%\displaystyle 18\% p.a.. What is future value?

Options

A1,83,677.68\displaystyle 1,83,677.68
B1,38,678.85\displaystyle 1,38,678.85
C1,83,776.53\displaystyle 1,83,776.53
D1,38,774.55\displaystyle 1,38,774.55
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Correct Answer

✅ Option b — 1,38,678.85\displaystyle 1,38,678.85

All Options:

  • A1,83,677.68\displaystyle 1,83,677.68
  • B1,38,678.85\displaystyle 1,38,678.85
  • C1,83,776.53\displaystyle 1,83,776.53
  • D1,38,774.55\displaystyle 1,38,774.55

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Detailed Solution & Explanation

Let the principal be P\displaystyle P and the annual interest rate be i\displaystyle i. The compound amount A\displaystyle A after t\displaystyle t years is: A=P(1+i)tA = P(1+i)^t We are given two amounts: 1. Amount after 2\displaystyle 2 years (A2\displaystyle A_2) = 5,100.5\displaystyle 5,100.5: P(1+i)2=5,100.5— (Equation 1)P(1+i)^2 = 5,100.5 \quad \text{--- (Equation 1)} 2. Amount after 4\displaystyle 4 years (A4\displaystyle A_4) = 5,203\displaystyle 5,203: P(1+i)4=5,203— (Equation 2)P(1+i)^4 = 5,203 \quad \text{--- (Equation 2)} Dividing Equation 2 by Equation 1: P(1+i)4P(1+i)2=5,2035,100.5\frac{P(1+i)^4}{P(1+i)^2} = \frac{5,203}{5,100.5} (1+i)2=1.020096(1+i)^2 = 1.020096 Taking the square root on both sides: 1+i=1.020096=1.011+i = \sqrt{1.020096} = 1.01 i=0.01 or 1% p.a.i = 0.01 \text{ or } 1\% \text{ p.a.} Now, substitute (1+i)2=1.0201\displaystyle (1+i)^2 = 1.0201 back into Equation 1 to find P\displaystyle P: P×1.0201=5,100.5P \times 1.0201 = 5,100.5 P=5,100.51.0201=5,000P = \frac{5,100.5}{1.0201} = 5,000 Thus, the principal P=5,000\displaystyle P = 5,000 and interest rate R=1%\displaystyle R = 1\%. Hence, **Option B** 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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If Rs. 1,000\displaystyle \text{Rs. }1,000 be invested at interest rate of 5%\displaystyle 5\% and the interest be added to the principal every 10\displaystyle 10 years, then the number in years in which it will amount to Rs. 2,000\displaystyle \text{Rs. }2,000 is:

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