Mathematics of FinanceMCQMTP Sep 24 Series IIQuestion 1427 of 512
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At what time a certain sum of money amounts to 400\displaystyle 400 at 10%\displaystyle 10\% p.a. S.I. and to 200\displaystyle 200 at 4%\displaystyle 4\% p.a. S.I.

Options

A10\displaystyle 10 Yrs.
B30\displaystyle 30 Yrs.
C50\displaystyle 50 Yrs.
DNone of these
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Correct Answer

Option c50\displaystyle 50 Yrs.

All Options:

  • A10\displaystyle 10 Yrs.
  • B30\displaystyle 30 Yrs.
  • C50\displaystyle 50 Yrs.
  • DNone of these

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Detailed Solution & Explanation

Let the principal amount be P\displaystyle P and the time period be T\displaystyle T years. The formula for Simple Interest amount (A\displaystyle A) is: A=P(1+r×T100)A = P\left(1 + \frac{r \times T}{100}\right) We are given two cases: 1. At 10%\displaystyle 10\% p.a. S.I., the amount is Rs. 400\displaystyle \text{Rs. }400: 400=P(1+0.10T)— (Equation 1)400 = P(1 + 0.10 T) \quad \text{--- (Equation 1)} 2. At 4%\displaystyle 4\% p.a. S.I., the amount is Rs. 200\displaystyle \text{Rs. }200: 200=P(1+0.04T)— (Equation 2)200 = P(1 + 0.04 T) \quad \text{--- (Equation 2)} Dividing Equation 1 by Equation 2: 400200=P(1+0.10T)P(1+0.04T)\frac{400}{200} = \frac{P(1 + 0.10 T)}{P(1 + 0.04 T)} 2=1+0.10T1+0.04T2 = \frac{1 + 0.10 T}{1 + 0.04 T} Cross-multiplying: 2(1+0.04T)=1+0.10T2(1 + 0.04 T) = 1 + 0.10 T 2+0.08T=1+0.10T2 + 0.08 T = 1 + 0.10 T 21=0.10T0.08T2 - 1 = 0.10 T - 0.08 T 1=0.02T1 = 0.02 T Solving for T\displaystyle T: T=10.02=50 yearsT = \frac{1}{0.02} = 50 \text{ years} Thus, the time period is 50\displaystyle 50 years. Hence, **Option C** 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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