Mathematics of FinanceMCQMTP Nov 20Question 1309 of 512
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What is the sum of money will amount to 1035.50\displaystyle 1035.50 in four years at compound interest for 1\displaystyle 1st, 2\displaystyle 2nd, 3\displaystyle 3rd and 4\displaystyle 4th years being 4%\displaystyle 4\%, 3%\displaystyle 3\%, 2%\displaystyle 2\% and 1%\displaystyle 1\% respectively?

Options

A10,000\displaystyle 10,000
B11,000\displaystyle 11,000
C1035\displaystyle 1035
D11305\displaystyle 11305
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Correct Answer

Option a10,000\displaystyle 10,000

All Options:

  • A10,000\displaystyle 10,000
  • B11,000\displaystyle 11,000
  • C1035\displaystyle 1035
  • D11305\displaystyle 11305

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Detailed Solution & Explanation

**Derivation of Principal Amount** *Note: The question contains a typo in the amount value, stating it is 1035.50 instead of 11,035.50. We show the calculation using the correct amount of 11,035.50 which yields a matching option.* Given: - Future Value (A\displaystyle A) = Rs. 11,035.50\displaystyle \text{Rs. }11,035.50 - Time (t\displaystyle t) = 4\displaystyle 4 years - Compound interest rates: r1=4%\displaystyle r_1 = 4\%, r2=3%\displaystyle r_2 = 3\%, r3=2%\displaystyle r_3 = 2\%, r4=1%\displaystyle r_4 = 1\% **Step 1: Set up the formula for compound interest with varying rates** A=P×(1+r1)(1+r2)(1+r3)(1+r4)A = P \times (1 + r_1)(1 + r_2)(1 + r_3)(1 + r_4) 11035.50=P×(1+0.04)(1+0.03)(1+0.02)(1+0.01)11035.50 = P \times (1 + 0.04)(1 + 0.03)(1 + 0.02)(1 + 0.01) 11035.50=P×(1.04×1.03×1.02×1.01)11035.50 = P \times (1.04 \times 1.03 \times 1.02 \times 1.01) **Step 2: Compute the product** 1.04×1.03×1.02×1.01=1.103550241.04 \times 1.03 \times 1.02 \times 1.01 = 1.10355024 11035.50=1.10355024P11035.50 = 1.10355024 P **Step 3: Solve for P\displaystyle P** P=11035.501.10355024Rs. 10,000P = \frac{11035.50}{1.10355024} \approx \text{Rs. }10,000 *(If we use the literal question amount of 1035.50: P=1035.501.10355024938.33\displaystyle P = \frac{1035.50}{1.10355024} \approx 938.33.)* Hence, **Option A** 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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