Mathematics for FinancePYQ 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

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.

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A certain sum of money was put at S.I. for 2.5\displaystyle 2.5 years at a certain rate of S.I. p.a. Had it been put at 4%\displaystyle 4\% higher rate, it would have fetched 500\displaystyle 500 more. Find the sum of money.

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