Mathematics of FinanceMCQPYQ Sep 24Question 1265 of 512
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Kanta wants to accumulate 4,91,300\displaystyle 4,91,300 in her savings account after three years. The rate of interest offered by bank is 6%\displaystyle 6\% per annum compounded annually. How much amount should she invest today to achieve her target amount?

Options

A4,37,500\displaystyle 4,37,500
B4,09,600\displaystyle 4,09,600
C46,900\displaystyle 46,900
D49,600\displaystyle 49,600
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Correct Answer

Option b4,09,600\displaystyle 4,09,600

All Options:

  • A4,37,500\displaystyle 4,37,500
  • B4,09,600\displaystyle 4,09,600
  • C46,900\displaystyle 46,900
  • D49,600\displaystyle 49,600

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Detailed Solution & Explanation

**Derivation of Invested Principal** *Note: The question contains a typo in the interest rate, stating it is 6% per annum. The options correspond to a rate of 6.25% per annum (17/16=1.0625\displaystyle 17/16 = 1.0625). We present the mathematically clean solution using 6.25%.* Given: - Target Future Value (A\displaystyle A) = Rs. 4,91,300\displaystyle \text{Rs. }4,91,300 - Rate of Interest (r\displaystyle r) = 6.25%\displaystyle 6.25\% per annum compounded annually - Time (t\displaystyle t) = 3\displaystyle 3 years **Step 1: Set up the Compound Interest equation** A=P(1+r)tA = P(1 + r)^t 491300=P(1+0.0625)3491300 = P(1 + 0.0625)^3 491300=P(1.0625)3491300 = P(1.0625)^3 **Step 2: Express the term in fractions** 1.0625=17161.0625 = \frac{17}{16} 491300=P(1716)3491300 = P \left(\frac{17}{16}\right)^3 491300=P×49134096491300 = P \times \frac{4913}{4096} **Step 3: Solve for P\displaystyle P** P=491300×40964913P = 491300 \times \frac{4096}{4913} P=100×4096=Rs. 4,09,600P = 100 \times 4096 = \text{Rs. }4,09,600 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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