Mathematics of FinanceMCQMTP Sep 24 Series IIQuestion 1428 of 512
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6,400\displaystyle 6,400 amounts to 7840\displaystyle 7840 in two years at simple interest. How much will a sum of 84\displaystyle 84 invested at the same rate of simple interest amount in four years?

Options

A11.20\displaystyle 11.20
B112.20\displaystyle 112.20
C121.80\displaystyle 121.80
D121.80\displaystyle 121.80
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Correct Answer

Option d121.80\displaystyle 121.80

All Options:

  • A11.20\displaystyle 11.20
  • B112.20\displaystyle 112.20
  • C121.80\displaystyle 121.80
  • D121.80\displaystyle 121.80

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Detailed Solution & Explanation

First, let's find the simple interest rate of the first investment. Given parameters: * Initial Principal (P1\displaystyle P_1) = Rs. 6,400\displaystyle \text{Rs. }6,400 * Final Amount (A1\displaystyle A_1) = Rs. 7,840\displaystyle \text{Rs. }7,840 * Time (t1\displaystyle t_1) = 2\displaystyle 2 years The Simple Interest (SI1\displaystyle SI_1) earned is: SI1=A1P1=7,8406,400=1,440SI_1 = A_1 - P_1 = 7,840 - 6,400 = 1,440 The formula for Simple Interest is: SI1=P1×r×t1100SI_1 = \frac{P_1 \times r \times t_1}{100} 1,440=6,400×r×21001,440 = \frac{6,400 \times r \times 2}{100} 1,440=128r1,440 = 128 r Solving for r\displaystyle r: r=1,440128=11.25% p.a.r = \frac{1,440}{128} = 11.25\% \text{ p.a.} Now, we calculate the amount (A2\displaystyle A_2) for the second investment: * Principal (P2\displaystyle P_2) = Rs. 84\displaystyle \text{Rs. }84 * Rate (r\displaystyle r) = 11.25%\displaystyle 11.25\% p.a. * Time (t2\displaystyle t_2) = 4\displaystyle 4 years The interest (SI2\displaystyle SI_2) earned is: SI2=P2×r×t2100=84×11.25×4100=84×45100=37.80SI_2 = \frac{P_2 \times r \times t_2}{100} = \frac{84 \times 11.25 \times 4}{100} = \frac{84 \times 45}{100} = 37.80 The final amount (A2\displaystyle A_2) is: A2=P2+SI2=84+37.80=121.80A_2 = P_2 + SI_2 = 84 + 37.80 = 121.80 Thus, the amount is Rs. 121.80\displaystyle \text{Rs. }121.80. Hence, **Option D** 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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