Mathematics of FinanceMCQPYQ May 18Question 1175 of 512
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If Rs. 1,000\displaystyle Rs. \displaystyle \text{Rs. }1,000 be invested at interest rate of 5%\displaystyle 5\% and the interest be added to the principal every $10$ years, then the number in years in which it will amount to $Rs. \displaystyle \text{Rs. }2,000$ is:

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option a — $16 \frac{2}{3}$ years

All Options:

  • A$16 \frac{2}{3}$ years
  • B$16 \frac{1}{4}$ years
  • C$16$ years
  • D614\displaystyle 6 \frac{1}{4} years

Detailed Solution & Explanation

**Derivation of Time to Amount to Rs. 2,000** Given: - Initial Principal (P1\displaystyle P_1) = Rs. 1,000\displaystyle Rs. \displaystyle \text{Rs. }1,000 - Rate of Interest (r\displaystyle r) = 5%\displaystyle 5\% per annum - Period after which interest is added to principal = $10$ years **Step 1: Calculate the amount at the end of the first $10$ years** The simple interest (I1\displaystyle I_1) earned in the first $10$ years is: I1=P1×r×t1100=1000×5×10100=Rs. 500I_1 = \displaystyle \frac{P_1 \times r \times t_1}{100} = \frac{1000 ×\displaystyle \times 5 ×\displaystyle \times 10}{100} = Rs. \displaystyle \text{Rs. }500 At the end of $10$ years, this interest is added to the principal to form the new principal. New Principal (P2\displaystyle P_2) = P1+I1=1000+500=Rs. 1,500\displaystyle P_1 + I_1 = 1000 + 500 = Rs. \displaystyle \text{Rs. }1,500 **Step 2: Calculate the time needed for the amount to reach Rs. 2,000** Target Amount = Rs. 2,000\displaystyle Rs. \displaystyle \text{Rs. }2,000 Required Interest (I2\displaystyle I_2) in the second period = Target Amount−P2=2000−1500=Rs. 500\displaystyle \displaystyle \text{Target Amount} - P_2 = 2000 - 1500 = \text{Rs. }500 Let t2\displaystyle t_2 be the additional number of years required: I2=P2×r×t2100I_2 = P2×r×t2100\displaystyle \frac{P_2 \times r \times t_2}{100} 500=1500×5×t2100500 = 1500×5×t2100\displaystyle \frac{1500 \times 5 \times t_2}{100} 500=75×t2500 = 75 ×\displaystyle \times t_2 t2=50075=203=623 yearst_2 = 50075=203=6\displaystyle \frac{500}{75} = \frac{20}{3} = 623\displaystyle \frac{2}{3}  years\displaystyle \text{ years} **Step 3: Calculate the total time** Total Time=t1+t2=10+623=1623 yearsTotal Time=t1+t2=10+6\displaystyle \text{Total Time} = t_1 + t_2 = 10 + 623=16\displaystyle \frac{2}{3} = 1623\displaystyle \frac{2}{3}  years\displaystyle \text{ years} 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.

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